Fenerbahçe have been in talks with Andre Villas Boas according to the Milliyet newspaper.
Boas won the Russian league title with Zenit St Petersburg this season but was criticised for playing unattractive football.
Boris Chukhlov, who won the Soviet title with Zenit in 1984, told the BBC that Villas-Boas plays anti-football.
“Zenit play boring football,” Chukhlov said.
“A team full of star names is going out onto the pitch, however, the tactics are too cautious. The side is showing anti-football, which basically boils down to giving the ball as quickly as possible to Hulk or Danny.”
The former Chelsea boss guided Zenit to second last season and won the 2014-15 league campaign but the team was knocked out of the Champions League stages.
Villas-Boas has previously coached at Chelsea, Tottenham and enjoyed a successful spell at Porto.
Fenerbahçe finished the league season as runners up and were beaten to the race to win the league title for the 20th time by bitter rivals Galatasaray.
Yellow Canaries boss Ismail Kartal has resigned from his position and the Istanbul giants are expected to appoint a foreign coach.