The Lions are reported to be using Wesley Sneijder as an intermediary to sway Van Perise’s decision.
Galatasaray could face competition from bitter rivals Fenerbahçe after it Milliyet claimed that the Yellow Canaries have stepped up efforts in their attempt to sign the Dutch star.
The 31-year-old striker recently stated that he does not want to spend another season as a rotation player.
“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.”
The Lions won the league title for the 20th time last season and went on to lift the Turkish Cup for the 16th time to win their sixth double.
Galatasaray will hope the lure of playing regular first team football, a lucrative contract and Champions League action will be enough to persuade Van Persie to join.