The former African Player Year joined the Istanbul side from Napoli last season and helped them win the Turkish topflight at the expense of rivals Fenerbahce and Besiktas.
Now the next goal is to make a point amongst Europe’s elite teams.
“I spoke with the president when I arrived here and we want to really make a statement in the Champions League,” Osimhen told Uefa website.
“We want to show that, in Türkiye, we are the team that the whole world will know this year because we actually did something amazing in Europe.
“We’ve dominated the league for years. We will keep on dominating it, but now it’s time to make a statement in the most prestigious games, Champions League games, because it’s beautiful when you play in the Champions League. So, for us, we want to make a statement.”
Galatasara bowed 5-1 to Eintracht Frankfurt in their first game of this season’s competition but bounced back to defeat Liverpool and Bodo/Glimt. They are guests of Ajax on Wednesday.