Williams engineering director Patrick Head has revealed that the team allowed Lewis Hamilton to slip through its grasp in late 2004.
Head told reporters that Hamilton and his father Anthony had approached Williams after a disagreement with McLaren three years ago.
The Williams co-founder says a deal with Hamilton fell through because the squad's then engine partner BMW declined to fund the young Briton's junior career as McLaren had.
The Hamiltons had not been keen on McLaren's plan to keep Lewis in the Formula 3 Euro Series for a second season - although he subsequently swept to a dominant title in the 2005 championship.
"They rang up and said 'Can we come and see you?'," Head was quoted as saying by The Guardian.
"And they came in and said 'Ron Dennis has dropped us'.
"We were with BMW at the time and I think Frank (Williams) rang (BMW's) Mario Theissen and said 'Look, this guy looks as if he could be pretty good and he has come to us saying can we help him?'
"And I think Mario said they weren't prepared to provide any support and we weren't in a position financially where we could finance his racing.
"So much to Frank's annoyance, he could have had Lewis in a Williams."
Frank Williams also revealed that McLaren attempted to sign Nico Rosberg to partner Hamilton after its split with Fernando Alonso last year.
But Williams said he had no intention of letting his lead driver go.
"It was never a thought we entertained," Williams was quoted as saying by Reuters.
"We had an offer of majestic proportions but it was never ever discussed.
"Why would we give away the crown jewels?
"Why bother improving the car by one second if we then give away half a second with the driver?"