Turkish television station TRT Spor are reporting that Fenerbahce have begun attempts to sign the 23-year-old former Real Madrid trainee - with a potential initial loan deal in mind.
The same outlet however also report that Spanish side Villarreal are interested in a permanent deal - who Norwich have dealt with this summer, signing left-back Xavi Quintilla on loan with a view to the deal being made permanent if promotion can be secured.
The Istanbul club finished seventh in the Super Lig last season and the 19-time champions have not won their domestic title since 2014.
Buendia enjoyed a brilliant first season in England when he scored eight goals and assisted 17 in 41 games in all competitions, as Norwich won the Championship title.
He had been signed from Spanish side Getafe for around £1.5million, which reportedly rose to around £5m once add-ons had been factored in for promotion to the Premier League.
He managed seven assists but just one goal in 36 games in the top flight last season, being dropped to the bench mid-season after some costly errors and being sent off in the penultimate game of the relegation campaign for a frustrated elbow in the back of an opposition player during a home defeat to Burnley.
He is under contract until 2024 but spoke out earlier this month to say that he would be interested in leaving for a club at a higher level - but that he was fully committed to the Championship cause while still a Norwich player.