The Spanish football magazine claims that the Turkish international is available for sale with Turan is struggling for games at Barcelona.
Don Balon go onto state that Mourinho is a long term admirer of Turan and that he has set his sights on signing Ivan Rakitic and Marc Bartra as well.
However, move for Turan looks unlikely given that the 29-year-old only moved to Barcelona last summer and only made his debut this year.
Turan also recently told the Turkish newspaper Hurriyet that he turned down a move to England in favour of joining Barcelona.
Barcelona are unbeaten in their last 32 games. Turan made his debut for the club against rivals Espanyol in the Spanish Cup. Barca won the game 4-1 and the bearded winger started on the right side of midfield.