According to local media reports, Kaka met Mourinho and Real director general Jose Angel Sanchez on Monday and was told he was not guaranteed a place in the starting line-up this season and should seek alternative employment.
The 2007 World Player of the Year, who joined Real from AC Milan for a fee of around £56 million three years ago, has been linked with a move to Paris Saint-Germain, the Ligue 1 club coached by his former boss at Milan Carlo Ancelotti.
Other reports have pegged him as a potential makeweight in a deal to bring Tottenham Hotspur's Luka Modric to the Bernabeu.
A Real spokeswoman said the club's press office had no information on the reason for Kaka's omission from the squad.
The 30-year-old has shown flashes of his former brilliance during his stint in Spain but has been sidelined several times by injury and mainly played second fiddle to German international Mesut Ozil last season.
He suffered a miserable end to his 2011-12 Champions League campaign in May when he had a penalty saved in the semi-final shootout against Bayern Munich as Real crashed out to the Bundesliga side.