The Chronicle reports that Newcastle United are also interested in recruiting the former Arsenal star as their next head coach.
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.
The Istanbul giants recently appointed Italian sporting director Giuliano Terraneo which indicates that they will bring in a foreign manager.
Fenerbahçe have won the league title 19 times and will be aiming to match bitter rivals Galatasaray’s tally of 20 championships next season.