The Turkey international has been strongly linked with a summer move from the Santiago Bernabeu, with Arsenal reportedly keen on a season-long loan deal.
Sahin joined Real from German champions Borussia Dortmund last summer but failed to make a major breakthrough in the first team, making just four appearances in Los Blancos’ triumphant Primera Liga campaign.
Mourinho has now claimed that should he want, the 23-year-old can leave the Spanish giants this month.
“The point is, he’s a young boy, he wants to play every match,” said the Portuguese. “He wants to play to be happy, and in Real Madrid with Xabi Alonso, with [Sami] Khedira, with Lassana [Diarra], [Esteban] Granero, [Mesut] Ozil, the situation is not easy.
“Real Madrid is very difficult. It is not an easy club, because we demand a lot. We have great players, and when you don’t start well, it is difficult to do it.
“If he stays, he’s not a problem for me, he’s one more solution. We leave [the situation] in his hands. Be happy.
“Decide what you want to decide, to be happy. If you decide to leave we are going to help you to leave. If you decide to stay, we are going to support you and try to succeed this season.”