But if she does, she would definitely prefer a less arduous route to the title, one that does not encompass the nerve-jangling fear of losing both a nine-stroke lead and the title.
Five years ago, Gustafson played some of the finest golf of her career to be 12-under par after three rounds. Although the tournament was not then acknowledged as a major, it had a full field of world-class competitors and, after the Swede eagled the first hole of the final round, she held a nine-shot lead.
But gradually the shots began to slip away and the more Gustafson tried to protect her lead - instead of playing the golf that gave it to her in the first place - the worse the situation got. In the end, she prevailed, but not before seven shots of her original margin had disappeared.
The memories of that near nightmare resurfaced yesterday for Gustafson, as she returned to something near her best form and, on a day made desperately difficult by heavy rain and driving wind, got round in 69, three-under par, to be only one behind the surprise leader, Jeong Jang.
The latter, a diminutive Korean known by her peers as JJ, is one of 26 players from that country with cards to play the LPGA tour.
In her sixth season as a professional, she has yet to win but she showed something of the right attitude yesterday when told by her caddie: "You have to smile today." She replied: "I have to?" And the caddie said: "Yes, because everyone has the same conditions."
As a formula, it worked, and she responded with an eagle, four birdies and just two bogeys.
Gustafson is having a middling-to-poor season in the US. After 14 tournaments she is 56th in the official money list, without a win and with only two top-10 finishes. But a 69 in the final round of last week's Evian Masters brought back some confidence and she said: "Birkdale is my favourite course and I think that I have been playing better than my scores have shown."
Some of the big names suffered the most in the morning gales. Annika Sorenstam, attempting to win her third major of the season, did well to contain the elements sufficiently for a 73 - one-over par - and said: "It was very, very difficult, really tough."
The Swede, who had been reaching all the par fives in practice, suddenly found them out of range and failed to birdie any of the three that form part of Birkdale's last four holes.
Michelle Wie managed a 75, three-over. She said: "I have played in rain before. I have played in the wind before. I've played when it was cold before. But with all of them together, it was hectic. This is the first time I've played in the British Open and I feel like I got the whole package."
There was a one-hour rain delay while Wie was on the course, meaning that not all the field will finish. The defending champion, Karen Stupples, quickly discovered, though, that fame is fleeting. Her group consisted of the winner and runner-up last week at the Evian Masters, Paula Creamer and Lorena Ochoa.
Both were correctly named on the carry board telling the spectators how the players were doing. Karen, though, was simply "Tupple" although the lack of an "S" or two probably had nothing to do with three putts from 15-feet for a bogey at the short fourth.
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