The legendary Portuguese manager has been linked with a move to the Premier League in recent weeks and now with his side 5 points behind leaders Galatasaray he could be looking for a new role.
Muslera believes this would be for the best for Turkish football and says Mourinho's actions have offended many who want him out of the league entirely.
“The insults towards Turkish football and the fact that he is attacking some referees are things that bother me,” Gala captain Muslera told Turkiye Today.
“This is the first time in 14 years that I feel obliged to make such a speech. I won 17 trophies in 14 years. If we consider my contribution, my constant aim is to advance Turkish football.
“If Mourinho, who came here 4 months ago, criticises Turkish football and doesn't like it, he can leave. Although nobody says anything, I think now someone can say something to him. We need to pay a little more attention to those who move Turkish football forward.”
Speaking after his Fenerbahce side’s 1-1 draw against former club United in the Europa League, Mourinho hinted that he wanted to leave and had unfinished business in the Premier League.
"The best thing I have to do is when I leave Fener is that I go to a club that doesn’t play in UEFA competition. So, a club at the bottom in England who needs a coach in two years, I’m ready to go.”