Galatasaray board member Cuneyt Tanman was reported to have travelled to England recently to hold talks with the Dutchman's agent.
The Dutch duo are understood to have a close relationship, but Van Gaal's managerial philosophy should mean Van Persie will be moved on unless he is seen as an asset.
Ever since Sir Alex Ferguson's retirement in 2012 when Van Persie won his first Premier League medal, the striker has looked out of favour with a lack of goalscoring form and problems with injuries.
Galatasaray manager Hamza Hamzaoglu has confirmed that they are interested in signing the 31-year-old, though, after winning the Turkish Super Lig last season.
“We want to sign players who will both improve the squad and excite our fans. No manager would be able to say no to van Persie,” Hamzaoglu told Manchester Evening News.
“However, we cannot spend beyond our means. We hope to come to an agreement with him.”
A lot of blame was put on David Moyes last season when several players, including Van Persie, were not performing. Although, last season there can be no excuse. He teamed up with his preferred former international boss, received opportunities and never really delivered.
The question many will ask is whether the former Arsenal captain is past his best. Robin van Persie provided some memorable moments for Manchester United and if he were to be sold this summer, he will be remembered fondly by the Old Trafford faithful.