The Chile international is understood to be free to leave the Camp Nou despite his World Cup heroics, with the imminent arrival of Luis Suarez set to add to the vast levels of competition for a starting berth at the club.
Arsenal are thought to be leading the race for the 25-year-old, with the player himself having declined the chance to be involved in the deal between the Spanish giants and Liverpool.
Juventus are also keen, but the Italians may be unable to match the salary Sanchez could earn at the Emirates Stadium.
But now United are also in the battle, and are willing to pay big to land the South American.
Louis van Gaal is understood to be ready to splash the cash to improve his inherited squad, and he sees Sanchez as a good option.