The La Liga champions have been keeping close tabs on the 20-year-old central midfielder and were recently reported to be in talks with the Turkish international.
Arda Turan is reported to have contacted Tufan and encouraged him into joining the Spanish giants at the end of the season.
Borussia Dortmund have also been closely linked with the 20-year-old according to Sport Bild.
The Bursaspor midfielder has established himself as a first team regular for Bursaspor and has already broke into the senior Turkish national side.
Tufan midfielder has three goals and eight assists in 35 appearances for Bursaspor this season.
The versatile midfielder can play in defensive and attacking midfield roles as well as on the flanks as a winger and full back.
Bursaspor are currently fourth in the Süper Lig on 44 points and have scored the highest number of goals in the league this season – 52.