Fenerbahce boss Mourinho is relishing the task of taking on Osimhen again, with the sides meeting at The Sukru Saracoglu Stadium on September 21.
Mourinho's side are currently top of the table with 11 points, with Galatasaray two points adrift but with a game in hand.
Galatasaray will be boosted by the arrival of Osimhen, who scored 76 goals in 133 games for Napoli.
Jose Mourinho says he has 'one problem' with new Galatasaray signing Victor Osimhen
Mourinho previously faced Osimhen when managing Roma against Napoli.
Osimhen ended up leaving Napoli on a temporary basis after falling out with manager Antonio Conte.
Mourinho stated that he has a good relationship with Osimhen, but complained that the 25-year-old 'dives too much'.
'In fact, we have a very good relationship. But every time I play against him, I speak with him because I don't like the way he behaves. He dives too much.'
Mourinho added that he spoke to Osimhen about his diving when Roma faced Napoli last season.
He said: 'I told him, 'Look, you are one of the two best African players, you and (Mohamed) Salah.
'In the past, Didier Drogba, Samuel Eto'o, George Weah. You cannot behave like this. He dives too much. That's my problem with him.
'But after 10 minutes, we are fine. We have a very good relationship and for the Turkish league it's fantastic and for Galatasaray it's fantastic too.'
Osimhen will be hoping to make his debut for Galatasaray at home to Rizespor on Saturday.