Osimhen is on-loan at Gala from Napoli this season and is available for a set price of €70m courtesy of a clause in his contract.
Turkish journalist Serdar Ali Celikler has stated on NEO Spor that Osimhen has reached terms with United. However, no agreement between United and Napoli has been struck.
Osimhen's contract has just over a year to run and there's a belief that Napoli would be willing to sell for £25-30m.
The Nigeria international has scored 29 goals in 34 games for Gala this season, including 21 in the Super Lig.