"I don't know if he will stay or not, and neither he nor the team know either," Mourinho said at an awards ceremony in Lisbon.
"There are no doubts between us, he knows what I think and I know what he thinks," added the Portuguese, according to the Real website (www.realmadrid.com).
"As long as he is our player, and it's possible that he will stay another season, he will contribute.
"If he stays I'll be delighted and he will come to the U.S." on our pre-season tour.
Mourinho included 2007 World Player of the Year Kaka in his squad for Real's friendly at Benfica later on Friday but the 30-year-old is widely expected to move on after three largely disappointing seasons in the Spanish capital.
He has shown flashes of his former brilliance since joining from AC Milan for around 65 million euros ($79.95 million) but has been sidelined several times by injury and mainly played second fiddle to German international Mesut Ozil last season.
He has been linked in media reports with a move to Paris St Germain, the Ligue 1 club coached by his former boss at Milan Carlo Ancelotti, as well as a loan deal back to Milan and even a move to MLS side New York Red Bulls.
Mourinho was also asked about Real's Turkey midfielder Nuri Sahin, who has barely featured since joining from Borussia Dortmund a year ago.
Sahin is poised to join English Premier League side Arsenal on a loan deal, various Spanish media reported on Friday, without naming their sources.
Mourinho said he needed to trim one name from his squad and that he always tried to be honest with his players.
"Nuri is living in the grey zone and if he gets a good chance to play we believe it's better for him to leave and play elsewhere this season," he said.