Ryan Giggs reportedly met with executive vice chairman Ed Woodward on Monday to discuss his long-term future at Old Trafford.
A number of ex-players and supporters have called on the current Premier League champions to appoint Giggs on a permanent basis following David Moyes's sacking last week.
Giggs was named interim boss for United's final four games of the season, his first of which resulted in a 4-0 triumph over Norwich City on home turf last weekend.
Widespread reports have claimed that United will appoint Netherlands boss Louis van Gaal next week, but the club are hopeful of keeping Giggs within the coaching setup in some capacity.
According to the Daily Mail, Giggs and Woodward discussed the Welshman's potential role under Van Gaal, but the club will not force their new boss to include the veteran in his immediate backroom team.
Reports have claimed that the club may offer Giggs a one-year playing contract but are keen to keep the 40-year-old, as well as ex-players Paul Scholes and Nicky Butt, at the club in some role.
