The article states that the Yellow Canaries newly appointed sporting director Giuliano Terraneo has been in contact with Vieira and wants to see the former Arsenal man at Fenerbahce next season.
The news comes amid reports that Patrick Vieira is out of the running to become the new head coach of Newcastle United.
The Manchester City Under-21 chief completed his UEFA Pro License last week and is believed to be considering moving into first team management.
Viera won the Premier League title with Arsenal and the World Cup as well as the European Championship with France.
Fenerbahçe finished the league season as runners up and booked a place in the Champions League play-off stages.
The Yellow Canaries will participate in European competition for the first time in two years after serving their UEFA suspension.
Fenerbahçe have won the league title 19 times and will be aiming to match bitter rivals Galatasaray’s tally of 20 championships next season.