Robbie Fowler has suffered frustration at Anfield
Fowler is believed to have signed a five-year deal which will keep him at Elland Road until 2006.
But the former Kop hero has yet to undergo a medical which will seal the deal.
Leeds chairman Peter Ridsdale said: "Given the thoroughness of our medicals which normally take a full day to complete, I can see it being Thursday before we can even consider completing the transfer."
The Yorkshire club originally refused to pay the £15m that Liverpool were asking for, but the Merseysiders confirmed on Tuesday evening that a fee had been agreed.
The 26-year-old England striker has long been linked with Leeds, with manager David O'Leary constantly insisting he needs to strengthen his squad.
The Fowler deal would take his spending to £96.3m in three years - and the move has been welcomed by Leeds fans.
Leeds supporters' club chairman Ray Fell said: "If you are looking at bringing in a striker, then we've gone for one of the best.
"His record proves what an outstanding talent he is, and all the Leeds fans I have spoken to so far are delighted he is coming to Leeds - and we've got him at a bargain price.
"Goals are obviously a vital part of the game and what Robbie Fowler brings to Leeds is consistency, someone who can put the ball in the net on a regular basis.
"We're now definitely back as a big club, with the likes of Robbie Fowler playing alongside Rio Ferdinand.
"Obviously what we all want to see now is a trophy, and while all the clubs with strong squads are looking to win something, the Leeds fans are hoping this season is a breakthrough season.
"Maybe not the championship, but certainly we're looking for some sort of trophy."
Fowler has had a turbulent relationship with Liverpool's management, including a well-publicised training ground bust-up with assistant manager Phil Thompson earlier this season.
O'Leary's move came after he had earlier branded striker Alan Smith's disciplinary record "disgraceful" - and the possible Fowler deal must raise further question-marks about the England striker's Elland Road future.
Robbie Keane and Mark Viduka have been Leeds' first-choice striking partnership.
Keane and Viduka have scored just two Premiership goals apiece this season and O'Leary clearly wants to add firepower to his squad.
With Michael Bridges still a long-term injury victim and Smith banned for three matches, the club is short of top-quality competition up front.
Fowler has only had limited first-team opportunities this season.
And Liverpool may have taken the decision to sell him rather than risk a Steve McManaman-style Bosman free transfer departure when his contract runs out in 18 months' time.
Fowler's future has been shrouded in uncertainty for months, and earlier this season he was forced to make a public apology after a training ground row with Thompson.