The 29-year-old trained with the north London club on Friday as they prepare for the league tie against Crystal Palace on Saturday. According to the Mirror, the attacker has already said goodbye to his teammates at the hotel on Friday evening.
Sanchez had left Arsenal's team hotel before 11pm local time and is expected to be in Manchester on Saturday to complete his medical ahead of his switch to Old Trafford. Arsene Wenger had initially included him in his 19-man squad for the Eagles' trip to the Emirates this weekend.
The Mirror reports that Arsenal forced United by initially picking Sanchez to face Palace. However, a dramatic late night twist saw the former Barcelona player dropped from the squad for the fixture on Saturday.
Henrikh Mkhitaryan is also edging closer towards completing a switch to the Emirates. The Armenian international, who joined the Red Devils from Borussia Dortmund in 2016, will leave Old Trafford after a brief spell.
The 28-year-old has also said his final goodbye to his United teammates ahead of his impending move to Arsenal. It is believed that Mkhitaryan has agreed personal terms with the north London club.
Wenger confirmed in his pre-match press conference the swap deal involving Sanchez and Mkhitaryan is likely to be completed. His United counterpart Jose Mourinho admitted the Red Devils are "there" in sealing a deal for the South American star.
Initial reports suggested that United and Arsenal will conclude swap deals that will see Mkhitaryan and Sanchez moving in the opposite direction. However, the Mirror now claims that the complexity of swap deals has forced the two clubs to do two separate deals.
Arsenal face Palace and United take on Burnley on Saturday. Should both the deals for Sanchez and Mkhitaryan take shape before the kick-off, they will not be eligible to make their debuts on 20 January.