Defender Raphael Varane is at the top of the list of players who is considering an exit and has interested Manchester United.
Gareth Bale has endured a difficult time in the Spanish capital and could make a return to the Premier League.
And Isco, who failed to break into the side under Solari, could also be heading for the exit.
Karim Benzema, despite a prolific season in front of goal, is the final player who could bring an end to his Real career after a decade in Madrid.
Meanwhile, former Real defender Alvaro Arbeloa has said he feels sorry for Bale who has come under intense criticism for his performances.
“I think Bale has not been able to sell his commitment towards Real Madrid to the outside world,” Arbeloa told El Chiringuito .
“He can speak Spanish, but he doesn’t feel comfortable doing it with the media.
“He has scored some very important goals for the club and I feel that he gets criticised so much.”