The England international had been linked with a move away from Old Trafford throughout the summer, after asking former manager Sir Alex Ferguson for a transfer.
Rooney has since rediscovered his best form under new boss David Moyes and according to The Mirror, he is now open to discussions over a new deal.
There are 20 months left on Rooney's current £250,000-per-week contract but with the likes of Paris Saint-Germain and Chelsea interested, United are thought to be keen to extend the deal.
Rooney has privately agreed to forget his differences with Ferguson, who remains a director at the club, and concentrate on helping the team.
The forward scored as United came from 2-1 down to beat Stoke City 3-2 on Saturday afternoon.