The report claims that Turan is up for sale and that the La Liga champions are willing to take a loss on their star man to free up the wage bill following the arrival of Denis Suarez from Villarreal.
Turan joined Barcelona on a £29 million move last summer from Atletico Madrid and does have another four-years remaining on his contract.
The bearded winger 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.
Barcelona boss Luis Enrique did use Turan throughout the second half of the season but he was not given a starting role in key games over the course of the of 810 minutes of La Liga football he played over the league campaign.
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.