The incident occurred at the end of the Turkish Cup quarter-finals on Wednesday, which Mourinho's side lost 2-1 at home.
In February, Galatasaray accused Mourinho of 'racist statements' after he said the home side's bench had been "jumping like monkeys" following a 0-0 Super Lig draw.
Fenerbahce said that Mourinho's comments were taken out of context.
While it was not clear which statements Galatasaray were referring to, Mourinho said the home side's bench had been "jumping like monkeys" and that the match would have been a disaster if a Turkish referee had been in charge.
Fenerbahce coach Jose Mourinho said the Video Assistant Referee went from being the invisible man to the most important man on the pitch after several controversial decisions went against his side in their 3-2 Super Lig win at Trabzonspor on Sunday.
Manchester United will travel to Turkish giants Fenerbahce, now coached by Jose Mourinho, among their eight games in the league phase of the new-look Europa League, the draw for which took place in Monaco on Friday.
The club's last league title dates back to 2014.
"Good evening Fenerbahce fans, see you tomorrow at Kadikoy (the Istanbul suburb where the club is based) and let's start our journey together," Mourinho announced.
Mourinho was 41 when he left Porto and took over at a Chelsea side poised to dominate English football following Roman Abramovich's takeover. Now Amorim, at 39, is the favourite to replace Jurgen Klopp at Liverpool.
“I am Jose Mourinho and I don’t change. I arrive with all my qualities and my defects,” Mourinho said it back in 2010 when he was announced as the manager of Real Madrid.
Paulo Dybala scored twice as Roma eased to a 4-0 thumping of Cagliari at the Stadio Olimpico on Monday to notch a third straight Serie A win under Daniele De Rossi.
The 40-year-old former Italy midfielder returns to his hometown club where he spent almost his entire playing career
Mourinho departs Roma after an emotional two-and-a-half years in which he won Europa Conference League in 2022, ending a 14-year trophy drought for the capital club..
Roma coach Jose Mourinho has dismissed any notion of becoming Brazil's next manager, saying his allegiance is with his Italian Serie A side.
Roma have just one win from their six league matches so far.
“I thank you for the invitation to join the UEFA Football Board, but I regret to inform you that I will be relinquishing my involvement with immediate effect,” Mourinho wrote in a letter to UEFA director and former AC Milan chairman Zvonimir Boban.
AS Roma head coach Jose Mourinho has been suspended for their next four matches in the Europa League after the Portuguese boss directed abusive language at referee Anthony Taylor while the club was fined, Europe's soccer body UEFA said on Wednesday.
UEFA began disciplinary proceedings on Friday against AS Roma coach Jose Mourinho for using insulting and abusive language against the referee in the Europa League final against Sevilla.
His message was one of pride, which is what he has restored at Roma, a team which has one of Italy's largest, most passionate fan bases but has won little of note since being founded in 1927.