He told Sport Mediaset, Kavukcu revealed that the Turkish side will do everything they can to sign the 26-year-old, who is on loan from Napoli, permanently, but they will face some tough competition.
Kavukcu said: "Osimhen will announce his decision in April. At the moment, five of the world’s top clubs are interested in him.
“His arrival here was a dream - he came, and for now, he is playing with us. In January, there was talk of a transfer, but he stayed.
“He loves Galatasaray very much. Right now, he is the dream of all our rivals. Although we are focused on winning the title, we have not had direct discussions with Victor yet. There is no point in talking about it now.
“Galatasaray are a top-level club - if it weren’t, Victor wouldn’t have come. His stay at Galatasaray is not as impossible as it may seem."
The Nigeria international has been linked with the likes of Chelsea and Arsenal over the past few transfer windows.
Osimhen has impressed during his loan spell in Turkey, scoring 26 goals and providing five assists in his 30 games across all competitions.