"I don't think we will do anything in the month of January," Mourinho told a news conference before Saturday's La Liga game at Malaga.
"And I don't believe Kaka will go either," added the Portuguese. "If he stays it's good for the team."
Kaka joined Real from AC Milan for a fee of around 67 million euros ($88.3 million) in 2009, but has failed to reproduce the form that won him the World Player of the Year award in 2007 and has fallen behind German Mesut Ozil and newly-signed Croatian Luka Modric in the pecking order.
The 30-year-old has only started one game in La Liga, two in the Champions League and one in the King's Cup this season but appears willing to stay on and fight to win his place back.
Real have made a stuttering start to the defence of their La Liga title and last weekend's 2-2 draw at Espanyol left them in third after 16 matches, 13 points behind leaders and arch-rivals Barcelona and four adrift of second-placed Atletico Madrid.
"It doesn't help us thinking about being so far behind," said Mourinho, who appeared to write off his side's chances of a second consecutive league title after the Espanyol game.
"The only solution is to play each match with the intention of winning it and to improve," added the former Inter Milan, Chelsea and Porto manager.
"Everyone has to find the motivation and working as a group we should help each other and improve.
"Without shame I say that we are not happy with the statistics of recent months. We have to improve in everything."
Mourinho confirmed Fabio Coentrao would miss the Malaga game through injury, joining fellow left back Marcelo on the sidelines.
Malaga coach Manuel Pellegrini refused on Friday to be drawn into any discussion about Mourinho, who replaced him as Real coach in 2010.
"I have no relationship with him," the Chilean, whose team are fourth, told a news conference.
"It's an important match for me because we are five points behind Madrid," he added.
"The individual aspect has no significance. I am interested in the team, the global situation and getting three points."