The newspaper claims that Fenerbahçe are monitoring the situation at Chelsea closely and that they could make an offer should Mourinho part ways with the Blues.
The reigning Premier League champions are currently struggling in 15th place and have only managed to win 11 points from their last 10 games.
The report claims that Fenerbahçe are not happy with Vitor Pereira who was appointed over the summer transfer window.
Fenerbahçe have denied all previous rumours linking the club with another manager and have released statements in the past backing Pereira.
The Portuguese manager brought in several new players over the summer but despite not having time to fully gel Fenerbahçe are joint second in the Turkish Super League and doing well in the Europa League.