The Red Devils sold Nani to Fenerbahce at the start of last season after the Portugal international fell out of favour with former head coach Luis van Gaal.
However, a prominent Turkish news outlet DHA has reported that the Portuguese tactician wants Nani to return to United.
Nani has an €8 million release clause included in his current contract with Fenerbahce which has two years left to run.
The Portuguese international won four league titles and the Champions League at United before departing last summer.
Nani would become the first Portuguese player in the senior team to join Mourinho at United if he were to make the move.
Nani scored 13 goals and provided 12 assists in 46 appearances for Fenerbahce this season. The Portugal international has two years remaining on his contract with the Yellow Canaries.