The Spanish giants will try to tempt Liverpool and Chelsea into a move for Rafael van der Vaart, while one-time Manchester United targets Mahamadou and Lassana Diarra are both up for grabs.
Fernando Gago is also available, though attempts to spark interest from Manchester City are doomed, while Everton could only afford a loan or cut-price move for the Argentina midfielder.
Open to offers: Real Madrid want to offload a host of fringe players including Holland midfielder Rafael van der Vaart this summer
Madrid general director Jorge Valdano has drawn up the list of rejects after completing the £12.5million signing of Germany World Cup star Mesut Ozil from Werder Bremen.
Mourinho has also added Angel di Maria, Ricardo Carvalho, Sami Khedira, Sergio Canales and Pedro Leon this summer and must now reluctantly sacrifice players to raise funds and trim the squad.
Van der Vaart wants to stay and fight for his place - a decision welcomed by Mourinho - but Madrid paper Marca says Valdano has other ideas.
The Holland international could struggle for games following Ozil's arrival and the desire to give 19-year-old Canales some first-team experience rather than send him out on loan.
England expects: The likes of Lassana Diarra and Fernando Gago (R) could find Premier League club before the transfer window closes
Roy Hodgson is understood to be keen, but does not have a big budget to spend at Anfield, while links to Chelsea have gone cold and a return to Germany may be more likely for the former Hamburg player.
Former Chelsea, Arsenal and Portsmouth midfielder Lassana Diarra has also been linked to Liverpool, but Hodgson has already signed Christian Poulsen in anticipation of Javier Mascherano's departure.
United were also linked with Mahamadou Diarra in the winter and may still be in the market for a tough-tackling midfielder if the price is right.
Highly rated Argentina midfielder Gago should have no trouble finding a new home, but City, who tried to sign him in January, are unlikely to be interested after bringing in Yaya Toure from Barcelona.
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