Fellow Portuguese manager Vitor Pereira is currently head coach of the Yellow Canaries but his position remains precarious as Fenerbahce failed to win the league title this season.
Fenerbahce are no strangers to Mourinho and have maintained a close relationship over the years.
The Istanbul giants became the first foreign club to made Mourinho an offer back in 2003 and even held talks with him in Istanbul.
Mourinho: “Fenerbahce were the first foreign club to make me an offer to become their manager”
Fenerbahce opted to appoint the more experienced Christoph Daum instead who was sacked a season later.
Mourinho went onto become one of the most successful managers in world football and is currently considering his future after spending the last few months out of management.