The deal never came off, but it was a meeting that left a great impression on the Dutch international. Moreover, if he had joined the Red Devils, he would also have started leaving his own impression on opponents' egos some 11 years before he eventually arrived in the Premiership.
Davids' second-placed Tottenham play at Old Trafford tomorrow, leading the former Barcelona player to recall that discussion with Ferguson. "It was the best conversation I have ever had with a manager," he said. "I won't go into detail, but we spoke about general things. [You could say] I turned down the chance to work with him but it was 10 to 11 years ago. Do I have regrets? No, because I didn't do so bad in my career myself."
Having opted against the chance to play alongside Keane, five years later their paths did cross, on what proved to be a momentous fortnight for both players. In the Champions' League semi-final of 1999, Juventus picked up what looked like a decisive 1-1 draw in the first leg at Old Trafford. Two weeks later the "Old Lady" went two goals ahead and appeared to be cruising to her fourth final in as many years: but Keane had other ideas. The Irishman scored once and dragged United to victory, but he was booked and was suspended for the final. Given their similarity in style, it could just as easily have happened to the man nicknamed "The Pitbull".
The 65-times capped Davids prefers not to dwell on such defeats. Maybe also the memory of Old Trafford pains him as he lost the Champions' League final there in 2003 with Juventus against Milan.
A prickly character, the man who walked out on his country in Euro '96 has not changed much. He rebuffs statements that are put to him if they are not in the form of a question and picks out the next person to ask him something, like a teacher and his pupils. Some might call it arrogance, but having won the European Cup with Ajax a decade ago as part of the Kluivert, Seedorf, De Boer generation and then the scudetto in Italy, it is the arrogance of a successful footballer.
Davids, now 32, professed himself disappointed he would not be able to pit his wits once more against Keane, who is injured. But he will be up against Scholes, a player he still rates highly despite his own battles with his form. "Of course, it's disappointing that Keane is not playing, but Scholes will be. He is underestimated because I think he is the best of his type in the world. He's in the top 10. Even now he is one of the best. We all go through different phases in a season when different things happen to us, but he is still up there."
As if still scarred by the events at the Delle Alpi stadium all those years ago, Davids, who signed for Spurs on a free transfer from Internazionale in August, is expecting a hard fight. "What I like most about United, whenever I have watched them, is that they play with a big heart," he said. "In the big games it is always there. I like that. I like that attitude. When they have to be there, they are always there."
Of course, stepping it up is what his game has been all about for the past 10 years. And with Keane injured and United struggling in the title race, Ferguson will get a look to see if he should have had a second - and maybe more fruitful - conversation this summer with Davids.
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