Inler was linked with United, as well as rivals Manchester City, before he joined Napoli from Udinese in 2011, while more recently, Arsenal have been linked with the 29-year-old.
Just last month, Inler refused to be drawn on speculation linking him with a move to Arsenal during this month's transfer window, but according to TuttoMercatoWeb, United boss David Moyes is showing interest in the Switzerland international.
Moyes is widely expected to bring in at least one midfielder before the end of the month.
Speaking before Christmas, Inler had said of a move: "The transfer market? You will have to ask my agent, I do not pay attention to these things.
"I’m completely focused on my duties as a player."
Inler is under contract at Napoli until 2016.
