The 28-year-old has 18 months left on his current deal, but the club has contacted Rooney's representatives and the offer to start talks has been accepted.
Rooney - a summer target for Chelsea manager Jose Mourinho - is likely to be offered a new five-year deal on more than his current £250,000-a-week salary.
Mourinho this week sanctioned the sale of Juan Mata to Old Trafford, and there was speculation the new man's imminent arrival could increase Chelsea's chances of landing Rooney this summer.
That prospect now looks a distant one, and a new deal would take Rooney well into a second decade at Old Trafford.
Mata, meanwhile, flew north on Saturday and underwent a medical ahead of his club-record £40m move from Stamford Bridge.
The Spain international is expected to train with his new team-mates on Sunday, although the paperwork on the transfer cannot be completed before Monday.