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.
Mourinho, who was given his marching orders by referee Marco Piccinini at the start of the second half for dissent, said on Tuesday his reaction was caused by his treatment from the fourth official
Former Brazil boss Tite has been allegedly robbed in a street in Rio and then the thief blasted him over the country’s World Cup exit, Brazilian paper O Globo has reported.
Jose Mourinho has revealed the design of his new tattoo, which pays tribute to his European successes with Porto, Inter, Manchester United and Roma.
Jose Mourinho said that he and Roma had made history after winning the Europa Conference League on Wednesday, the club's first ever major European trophy.
Jose Mourinho said Tuesday that his experience of European glory will be no help to him as Roma are one step away from their first major continental crown.
Coach Jose Mourinho insisted that France’s World Cup winning midfielder Paul Pogba is happy to be back at Manchester United even as media reports had earlier claimed that he wanted a move away from Old Trafford.
Jose Mourinho has hit out at Manchester United's transfer window inactivity after watching his under-strength squad crash to a 4-1 defeat against Liverpool in the latest stop of their pre-season US tour.
Jose Mourinho suggests that Paul Pogba’s World Cup performance is the evidence of what he can do when he fully focuses on football. Mourinho insists that Pogba gave his best for his country team but he had not given his best for Manchester United.
Manchester United manager Jose Mourinho believes he can emulate Arsenal boss Arsene Wenger by coaching into his late 60s.
Manchester United manager Jose Mourinho insists European disappointment is nothing new for the English giants after losing 2-1 to Sevilla at Old Trafford to crash out of the Champions League by the same scoreline on aggregate.
