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 Madrid from German champions Borussia Dortmund last summer but failed to make any major breakthrough in the first team, making just four appearances in Los Blancos' triumphant Primera Liga campaign.
Mourinho has now claimed that 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."
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.