Ramsey has seen contract talks at Arsenal reach a standstill and looks to be heading out of The Emirates after 10 seasons at the club, with Old Trafford a possible destination.
The Wales midfielder has been linked with a host of top European clubs since the news of his likely exit broke, and the English publication now claim that the 'Red Devils' are a likely destination.
If this where to be the case it could be a case of third time lucky for United, who have twice previously wanted to sign the player.
He was widely linked with a move to the Manchester giants when he broke through at Cardiff, but chose a move to Arsene Wenger's Arsenal over linking up with Sir Alex Ferguson.
The reports also claim that the club tried to sign Ramsey this summer, but their enquiries were quickly rebuffed.
If the 27-year old does leave the 'Gunners' at the end of the season when his contract ends, he'll be free to go where he wants and interest in the goal scoring midfielder will doubtless be high.