The Brazilian scored twice for Real in a 4-0 friendly win at Deportivo La Coruna on Thursday night but said after the match he was hoping for a quick move away from the club.
"I want to leave. I think it’s the best thing for me and for the club. I'm trying to solve it before Monday” said Kaka.
The 31-year-old joined Real Madrid from AC Milan in 2009 for a then world record fee of £56m.
However, injuries have hampered his time in Spain and he has struggled to claim a regular starting place over the last few seasons.
A return to Milan seems the most likely option with the Italian giants long having talked of their desire to bring the player back to the San Siro.
He has also been linked with moves back to Brazil and also to the MLS.