Rooney was the subject of two failed bids from Chelsea last summer and is rumoured to be considering his future at Old Trafford.
United boss David Moyes has admitted Rooney may not sign a new contract if the Red Devils miss out on a top-four finish this season, and last week it was reported that Chelsea believe the England international's expiring contract will allow them to land him on the cheap at the end of the season.
However, Rooney is talking to United officials about an extension which according to widespread reports on Saturday morning would make him the highest paid player in the club's history.
And according to BBC Sport, the proposed new deal could keep the former Everton forward at the club for the rest of his career.
According to Saturday's report, United and Rooney hope to conclude contract talks in the coming week, ending talk about a summer switch to Stamford Bridge.
Paris Saint-Germain and Real Madrid have also been linked with Rooney in recent weeks, but Moyes insisted earlier this month that the player was still happy at the club.