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United have been linked with a move for the former River Plate man since last summer, when he produced some impressive performances for Chile at the World Cup.
Sanchez continued his form into the domestic season, scoring 12 goals in Serie A for Udinese.
It is understood that United chief executive David Gill met Gino Pozzo – the son of Udinese owner Giampaolo – in Barcelona on Tuesday to discuss a move.
Manchester City are believed to have recently bid £27 million for the services of the attacker often compared to former United star Cristiano Ronaldo, but his club are believed to be holding out for at least £30m, a fee City seem unwilling to meet due to the new financial fair play regulations coming into practice soon.
Giampaolo Pozzo just days ago claimed City are the favourites to land the Chilean, but Sanchez’s agent, Fernando Felicevich, has insisted it is far from a one-horse race.
He said: “Sanchez’s future is still wide open. After meetings with City, today we will have new appointments.”