The daily paper claims that the Catalan giants are considering a multi-million euro offer from an unnamed Chinese club for Turan.
Barcelona are understood to be open to recouping some of the €34 million spent on the Turkish international over the summer.
However, Barca boss Luis Enrique is reluctant to let go of Turan who he pushed the board to sign from Atletico Madrid over the summer.
Turan has settled in quickly to Barcelona after missing the first six-months due to the FIFA transfer ban imposed on the club.
The Turkish international has two goals and four assists in the 17 games he has featured in this season and still has another five years remaining on his contract.
The former Galatasaray star recently also claimed that he will remain at Barcelona next season.
“For me it’s a new system, a language that I still have to learn. Next year will be better,” Turan told Diario Ara.
“I know that from here I will be improving. Now it’s time to win titles and the year that comes will be better for me.”