The latest development comes just a day after Turan’s agent Ahmet Bulut revealed that his client would be staying at Barcelona.
Bulut stated that Turan still has another four-years left on his Barcelona contract and that he wants to remain.
Turan may want to stay but the latest reports suggest that the La Liga champions may consider an offer if the price is right.
The bearded winger has attracted interest from a number of Premier League clubs.
Recently appointed Manchester United boss Jose Mourinho is reported to have had Turan on his sights for the last few months.
Turan missed the first six-months of the season due to the FIFA transfer ban imposed on the club but still managed to lift two trophies including the La Liga and the Spanish Cup.
The bearded winger made 25 appearances in all competitions but struggled for playing time towards the end of the season.
Arsenal are reported to be interested in Turan according to Spanish sports newspaper AS.