TalkSport have reported that the former Juventus manager is already making preparations for next season and has placed the Turkish international on his transfer shortlist.
The report goes onto state that Conte is prepared to spend big for the 29-year-old in order to prise him away from Barcelona and fend off interest from China.
However, the flamboyant midfielder recently 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.”
Turan has settled in quickly to Barcelona after missing the first six-months due to the FIFA transfer ban imposed on the club.
Turan 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.