Roy Evans, the Liverpool manager, has made an initial offer of just over pounds 3m for the Norwegian, who has given the Dons notice that he will quit for nothing when his contract expires next summer.
The Wimbledon owner, Sam Hammam, is looking for a price closer to pounds 4.5m for Leonhardsen, but a compromise figure should soon be reached.
Leonhardsen is seen by Evans as the player to give his midfield some drive as their bid to sign Paul Ince from Internazionale looks like faltering on financial grounds.
Evans is also looking for a new striker and centre-back after this season's disappointments. He has the pounds 7m from Collymore's sale plus a further pounds 5m to spend.
The Liverpool manager has watched Polish striker Marek Citko, and he is also considering Derby County's Igor Stimac for his defence.
Aston Villa completed the signing of Collymore yesterday for a club record fee of pounds 7m. The deal takes the 26-year-old former Nottingham Forest forward's total transfer fees over the last four years to pounds 17.7m.
Collymore, who cost Liverpool a then British record pounds 8.5m when he moved to Anfield in June 1995, signed a four-year contract with Villa with a further one-year option.
"I used to support Villa as a boy so this is really a dream move home for me," said Collymore, who lives only 30 minutes from Villa's training ground.
West Ham are resigned to losing Slaven Bilic in a pounds 4.5m move to Everton today but their manager, Harry Redknapp, will use some of the money to offer Portuguese midfielder Hugo Porfirio a new deal to stay at Upton Park.
Porfirio's nine-month loan spell from Sporting Lisbon expired after the last Premiership game of the season at Manchester United on Sunday. But his contract with Sporting also runs out next month and West Ham's managing director, Peter Storrie, will meet the player and his agent tomorrow to negotiate a permanent free transfer to London.
Bilic, meanwhile, has still not formally announced his departure from West Ham but is expected to have a medical examination at Everton before completing a move which will make him one of the highest-paid defenders in the Premier League. West Ham will show a huge profit on the deal, having paid just pounds 1.6m to the German club Karlsruhe for Bilic only 18 months ago.
Bilic insisted he was reluctant to leave West Ham but wanted to join a bigger club capable of winning trophies. Everton finished below the London club in the final Premiership table.
Leeds have completed the pounds 500,000 signing of the Scottish international full-back David Robertson from Rangers. The Italian clubs, Perugia and Torino, were both keen to land the 28-year-old Robertson, whose contract at Ibrox has expired.
Peter Reid has pounds 6m to spend on the transfer market to spearhead Sunderland's promotion challenge back to the Premiership. The club's chief executive, John Fickling, yesterday gave Reid the nod to carry on as manager as Sunderland came to terms with the disappointment of relegation to the the First Division.
"Peter has done an excellent job for Sunderland Football Club and he's still got a job to do," Fickling said. "The pounds 10m we promised him is still available, less the pounds 3.8m he has already spent."