Nani is expected to complete the move by next week, but the two clubs are yet to agree a fee, with United wanting six million euros for the 28-year-old, who still has three years left on his contract.
The Portugal international is looking to move away from Old Trafford after being told that he was not part of manager Louis van Gaal's long-term plans.
Nani spent last season on loan with Sporting Lisbon and scored 12 goals in the 35 games in all competitions.
Sporting were initially interested in signing Nani on a permanent basis, but cooled their interest due to the price tag United put on the winger.
After Sporting dropped out of the race for Nani, Fenerbahce stepped in and head coach Vitor Pereira has pinpointed the 28-year-old as one of his top targets to sign this summer.