The Tabloid newspaper states that the Istanbul duo are “both ready to keep Van Persie on £220,000-per week and are readying three-year deals.”
United boss Louis van Gaal has been disappointed with his strikers this season and could make a number of changes in the summer.
“We have to improve. Improve in creating chances? No. Improve in finishing,” Van Gaal was quoted as saying by the Express after the 1-0 loss against West Brom.
Fenerbahçe have found sponsors that will finance the deal if Van Persie were to accept terms with the club according to the Milliyet.
The Netherlands international does however, want to stay at United next season according to the Daily Mail.
Van Persie will enter the final year of his United contract next season but the club have a policy of offering one-year deals to players over the age of 30.
The 31-year-old has three assists and 12 goals in 31 appearances for Manchester United this season.