However, Spurs will only countenance a straight sale for the Russian international, who has been told he can leave, and have rejected a bid by Zenit St Petersburg to take the 28-year-old on loan for six months.
Karim Benzema joins Real Madrid after snubbing Manchester United'The management were considering the loan of Roman Pavlyuchenko for six months to the summer in order to decide whether to buy him,' club president Alexander Dyukov said. 'Unfortunately this proposal did not suit Tottenham.'
Van Nistelrooy has been linked to a move back to the Premier League - having left Manchester United in 2006 - for some time and has sparked interest from Liverpool and Stoke City.
However, it is Spurs who have made the move and appear set to sign the player whose contract at the Bernabeu expires at the end of this season and who has barely featured this season.
He wants first-team football in order to make a bid to be in Holland's World Cup squad and recently turned down an offer to join Galatasaray.
Even though it is a free transfer, Spurs manager Harry Redknapp knows he will now have to move players on to help free up his wage bill especially as he is also keen to sign an experienced right-back.
It's understood that Spurs watched Bordeaux defender Mathieu Chalme during his club's 1-1 draw with Marseilles on Sunday.
Chalme, 29, is understood to be interested in playing in England although he may want to remain in France until the summer with his club still involved in the Champions League.
However, Spurs are hopeful, although they will have to also try to sell Alan Hutton, who has struggled since his move from Rangers two years ago and is available for around £4 million.
He has been offered to a number of clubs including West Ham and Hull City.