The Sun reports that United chief executive David Gill flew to Spain to seal the deal and the Red Devils are hoping to wrap up a £27million deal for the highly-rated winger.
United looks set to beat City, Barcelona and a host of other European giants.
Gill met Udinese president Gino Pozzo on Tuesday in Barcelona.
Sanchez’s agent Fernando Felicevich said: “An agreement with City? Sanchez’s future is still very much wide open.
“We are working on it and, after meetings with City, we have other new appointments.”