Although several clubs have been tracking the unsettled England striker, it is understood that Rooney is most attracted by the prospect of joining Jose Mourinho, a coach he has long admired, at Stamford Bridge.
United have maintained their stance that Rooney would not be allowed to leave for another English club, but a planned massive bid from Roman Abramovich may prompt the player to break the impasse and seek a move to the capital.
Arsenal and Paris St-Germain will also be monitoring the progress of the meeting between Moyes and Rooney, the first following the start of pre-season training. That meeting is expected to take place on Tuesday. Rooney and Moyes spoke after the Scot’s appointment was announced, but only now can they seek a resolution to what could become the transfer story of the summer.
Rooney will not wish to surrender bonuses with a formal transfer request, but that he has not declared a desire to stay has been telling. There is no doubt he is open to the idea of ending a nine-year association with United.
His future has been uncertain since the end of last season, when former United manager Sir Alex Ferguson suggested the 27-year-old had asked to leave, a claim that those close to Rooney have denied in private.

Moyes’s appointment was seen as having the potential to ease tensions, despite the pair’s tumultuous history at Goodison Park. Moyes and Rooney have patched up their differences in recent years, but Chelsea's strong interest will challenge any attempt to revive their working relationship.
With two years left on Rooney’s £250,000-a-week contract, there are both sporting and financial reasons for Moyes to consider a sale, despite the public pronouncements about wanting to keep him. To retain Rooney would sacrifice a significant transfer fee and raise the prospect of having to extend his lucrative deal.