The report goes onto state that Fenerbahce are currently in negotiations with both Campbell’s representatives and Arsenal.
Fenerbahçe have an ageing squad and are expected to bring in younger players over the summer transfer window.
The Istanbul giants could also face competition from rivals Galatasaray who have been keeping tabs on the Costa Rican international for the past two seasons.
Campbell received a number of offers last summer but Gunners boss Arsene Wenger wanted the 23-year-old to stay at the club.
The Costa Rica international had one goal in 16 appearances for the La Liga outfit this season.
The Yellow Canaries have secured a runners up place in the Süper Lig and booked a place in next seasons Champions League.