Spanish publication Sport claim that the newly appointed Chelsea manager Antonio Conte has set his sights on the Turkish international. The Sun states that the Italian tactician has promise him a key role in the team next season.
Turan turned down a move to Stamford Bridge in favour of a move to Barcelona last summer.
The 29-year-old joined Barcelona on a £29 million move from Atletico Madrid and does have another four-years remaining on his contract.
Turan has won every domestic title in Spain and Turkey as well as all European competitions trophies except the Champions League although he did reach the final with Atletico Madrid.
The former Galatasaray star missed the first half of the season due to the FIFA transfer ban imposed on the club but he did make 25 appearances since the turn of the year.