Yesterday, William Hill had him at 33-1 to lift the claret jug in the shadow of the Royal and Ancient Golf Club next Sunday, with Darren Clarke and Lee Westwood at 40-1. Justin Rose, deemed not long ago to be the likeliest major winner of the thrusting young Brit Pack that also includes Paul Casey and Nick Dougherty, has not even qualified. Donald, with his older brother, Christian, carrying his bag, has forged ahead of his contemporaries. The question is: can he also forge ahead of Tiger Woods, Ernie Els, Phil Mickelson and Vijay Singh? Does he have the game to become the first home-grown winner of the Open since Paul Lawrie's improbable win up the coast at Carnoustie in 1999?
Donald, currently rated the 14th best golfer in the world, certainly thinks so. "I finished third in the Dunhill Links at St Andrews last year, and I believe I've got as good a chance there as at any of the other Open venues, if not better. I feel comfortable around the place. I've played it quite a few times now and the course has really grown on me. I didn't care for it at first, but it plays so differently in different types of conditions, which is always a challenge. Technically, yes, you might change this or that on some of the holes. And it's frustrating when you get bad bounces. But you'll also get good ones. If you accept that then you will enjoy playing there."
Moreover, Donald has now shown that he has both the game and the temperament to make an impact in a major, playing the last eight holes in six under par to finish third - despite a second-round 77 - in this year's US Masters. "But it wasn't as if I ever had much chance of winning," he says. "I was still seven back of Tiger and [Chris] DiMarco. So I don't have experience of coming down the stretch in a major in strong contention. But I'm sure I would cope well with the pressure. I think pressure can be a good thing."
Peter McEvoy, who captained two Walker Cup teams in which Donald shone luminously, believes firmly that his protégé will be the next Brit to win a major. And Donald accepts the burden of McEvoy's expectation with a shy smile. "Peter's always been very kind to me," he says. "He's always said I would be very successful, and I do feel confident that I'm going to win majors. I believe I have the right mentality."
But there is the right mentality to win a major and the right mentality to win an Open at St Andrews. The last four men to triumph at the Home of Golf, Tiger Woods, John Daly, Nick Faldo and Seve Ballesteros, while wildly different personalities, were nothing if not implacable believers in their own talent. Donald, I fancy, is the same. And he has listened carefully to the only man alive to have won two Opens at St Andrews.
"I have gotten to know Jack [Nicklaus] a little, or at least gotten to the point where I can call him Jack rather than Mr Nicklaus. I'm a member of the Bears' Club, his signature course in Florida, and I see him there in the winter sometimes, as well on RBS days [golf days organised by the Royal Bank of Scotland, which sponsors both Donald and Nicklaus].
"I've watched the videos and heard his stories, about the majors he won, and the ones he didn't win. Mostly the majors he didn't win were won by other guys, in the sense that Jack didn't lose them. There was only one major that he thought he lost, after being in a position to win. He usually finished the job."
Of course, Nicklaus - to whom the Open Championship crowds will make a doubtless emotional farewell later this week (or, dare we imagine, next Sunday) - is unique in having won all four majors at least three times.
Donald, for all his ambition, knows that the precise, steady game acknowledged on the US Tour with the nickname "Plod", suits some championships better than others. "The US Open is probably my best bet. I keep it straight off the tee, and I play good tactical golf. Actually, that's why I did well at Augusta. I thought it was a long-hitters' paradise, but you've really got to position shots into the greens, and that's one of my strengths."
He told me that before this year's US Open at Pinehurst, North Carolina. So I watched with interest as he plodded to the top of the Pinehurst leader board on the first day, and cursed myself for not having had a small wager on him with the aforesaid Mr Hill. I then congratulated myself on my foresight when, after an opening 69, his scores got higher and higher and he finished with a miserable 80.
At last week's J P McManus charity pro-am in Ireland, however, Donald was sticking to his belief that the US Open, historically the hardest for non-Americans to win, is still the major to which his game is best suited.
"I needed to be more patient. I was attacking too many pins and pushing too hard. But it was only my second US Open. In future I'll stick to my game plan."
And what will be his game plan at St Andrews, about as difference a golf course from Pinehurst No 2 as it is possible to imagine?
"To keep it out of the bunkers. If there's no wind, it will come down to putting. If the wind is up, you've got to be patient, got to control ball flight. And be aware of certain places you mustn't be; where, if you're going to miss those big undulating greens, you shouldn't miss left, or shouldn't miss right, or shouldn't be short, or shouldn't be long. There are some holes there that fit your eye, in the sense that you don't think you can miss [the fairway] from the tee. And there are some, like 13, that are more narrow. I've had trouble on that hole before."
It is a fair bet that Donald will not be dwelling on past difficulties when he tees up on the par-four 13th on Thursday. He is a devoted practitioner of visualisation, conjuring a picture in his mind of the fine shot he is about to hit. All golfers visualise shots to some extent. Long before visualisation became the buzzword, Nicklaus used to talk about "going to the movies". But some, like Donald, do it much more zealously than others.
That he is also an enthusiastic artist is a help, he believes. "I work from photos I've taken, and my stuff is pretty realistic, with a bit of abstraction. I think the way you visualise a piece of art, how it's going to turn out, is the same as a golf shot. I can't explain how I'm going to hit a shot 230 yards straight, or how I'm going to paint something, but I can picture it in my mind."
It is a mind which, for the past 18 months, he has put in the hands of a psychologist called Jim Fannin, who preaches what he calls the SCORE system.
"It's not just helpful in sport. Jim teaches it to business people, too, or to people who just want to live their lives better. SCORE stands for self-discipline, concentration, optimism, relaxation and enjoyment. If you find a balance between those things then things will work out. And it has really helped my attitude on the golf course. I used to get upset too easily if I ever hit a bad shot, but I've worked with Jim on having a bit more fun out there. Look at Vijay. Do you ever see him angry? Jim has a five-second rule, meaning that the most important time on the golf course are the first five seconds after every shot. That's when you're trying to sell yourself positives rather than negatives. You tell yourself, 'I hit it solid, I hit it great, I'm a great player'. And if it's a bad shot, you tell yourself just to forget it and move on."
The demonstrable success of these mental disciplines in golf repeatedly confound those cynics who would dismiss them as so much psychobabble. On the other hand, there is something ever so slightly disconcertingly American about them, as indeed there is about Donald himself. His Home Counties accent has acquired an unmistakable Yankee twang, there too in the words he uses, such as "gotten", and the way he pronounces things, loading all the emphasis on the first syllable of "Ryder Cup", for example.
On yet another hand, no British golf fan should take pleasure in his achievements while lamenting the fact that they have an increasingly American provenance. Put simply, if he still lived near his folks in High Wycombe, rather than on the shores of Lake Michigan, he would be a fraction of the player he is.
"I've learnt so much over there," Donald says. "The guys are out on the range such a lot, and spend an enormous amount of time on their games.
"Sure, they have less fun on the US tour [than in Europe]. You get Miguel [Angel Jimenez] going to bed after a glass of wine and a Johnnie Walker, and you don't see that from the US players. Also, in Europe there's usually a specific hotel everyone stays at. You congregate in the bar and then everyone goes out for dinner. In the US there might be 20 hotels, and a lot of the guys fly in on private planes. Over there I hang out with my brother and some other caddies, and also Sergio [Garcia]. But I enjoy it both ways. When I turned pro, I never realised how much work you have to put in on your game."
For Donald, as for so many other players just below the mountain top, the guy on the summit offers the template.
"I watched Tiger, spent time figuring out what he did to play so well. He's probably the fittest, strongest guy out there, and that made me want to work harder at my fitness. So during tournaments I work out two or three times a week and harder in my off weeks. But Tiger's got a lot more inconsistent than he was five years ago. He never used to make mistakes. Now he drives it crooked sometimes. He still gets out of trouble better than anyone. But it gives the other guys, like Ernie and Vijay, a chance."
Modesty prevents Donald from bracketing himself with the guys who might capitalise on Tiger's occasional vulnerability, but he is undoubtedly one of them.
"I still have some consistency issues," he admits. "My bad shot is a left-left shot, where I get very active with my legs on the downswing. I hold the club too shut, get the angle of my wrists wrong. But I've been working hard on cutting that out, and I'm looking forward to getting to St Andrews to practise some of those shots you can't practise anywhere else - those long, lagging putts and chip-and-runs over the slopes and mounds. Playing St Andrews is like an exam. You hope you've studied all the right things."
He is 33-1 to graduate with first-class honours.