The newspaper report claims that Galatasaray will use his Netherlands national teammate Wesley Sneijder as an intermediary to convince the Dutch striker to join.
Galatasaray could struggle to meet the 32-year-old’s wage demands but would be able to offer first-team action and Champions League football.
Lions boss Hamza Hamzaoğlu recently signed a three-year contract extension and stated that the club will be targeting a striker over the transfer window.
The Netherlands international recently stated that he does not want to spend the next season on the peripheries of the team.
The star striker lost his place in United’s starting line up this season to Wayne Rooney.
“It is my ambition to play as many games as possible. I feel fitter than ever,” Van Persie was quoted as saying by Goal.
“I know that when you are at a club like Man United, you have to accept that you cannot always play or be guaranteed a starting place.
“I will take everything into consideration when I decide on my future and I know I have to be realistic about the situation.”
Galatasaray won the league title for the 20th time last season and went on to lift the Turkish Cup for their sixth double in club history.
Süper Lig rivals Fenerbahçe have also been closely linked with Van Persie.