United are reported to have already agreed personal terms with their former player according to Turkish media outlet DHA.
The bookmakers have also now priced United as favourites to sign the Portuguese intentional.
BetStars have made the Red Devils 4/5 odds-on favourites to re-sign Nani this summer just a year after selling him to Fenerbahce.
Trading director at BetStars Ian Marmion was quoted by CaughtOffside as saying: “All the talk at United since the Special One’s appointment has been on the likes of Zlatan joining the ranks at Old Trafford, but Nani has been backed heavily into 4/5 over the past 48 hours and looks set for a surprise return to the club.
“He struggled for form and fitness towards the end of his first spell with United but joining up with his fellow Portuguese countryman could turn out to be a very shrewd move.”
United would have to offer more than they sold Nani for just last year if they are to bring him back to Old Trafford.
Nani has a £6.2 million release clause for sides from the Premier League, La Liga and Serie A which would be more than the £4.2 million United received for him.
The experienced winger does still have another two-years remaining on his Fenerbahce contract but is reported to have fallen out with manager Vitor Pereira.