However, it's suggested the "urge to leave saw intermediaries get in contact with Manchester United to see if they were interested." Red Devils manager Jose Mourinho would reportedly be keen on Sanchez, though the player has a desire to link up with City boss Pep Guardiola again.
According to the report, while Sanchez had previously hinted he would accept another year at Arsenal, he's made a "conspicuous shift" and is now ready to push for a transfer.
It's noted that direct contact has been made between City and the Gunners about a possible deal for Sanchez. Both Sergio Aguero and Raheem Sterling are said to have been considered as potential makeweights in the transfer, although the Sky Blues are reportedly unwilling to lose either.
James Ducker of the Daily Telegraph reported City have lodged a cash-only offer of £50 million for Sanchez that has been rejected, though they will return with a bigger offer.
Football writer Liam Canning believes the Red Devils should be looking to sign the 28-year-old too:
Sanchez's future is set to be one of the most fascinating stories before the transfer window closes at 11 p.m. BST on Thursday.
Arsenal have a big decision to make on their star man. The forward is such an important part of their attacking setup as he scores goals, creates chances and runs opposition defenders ragged. If they were to lose him now, then replacing him would be an almost impossible task.
However, the prospect of seeing such a talented footballer leave for nothing next summer must be uncomfortable for the Gunners hierarchy, with his contract due to expire. And if City are to make another massive offer for the player, there will be a big temptation to cash in.
Bleacher Report's James McNicholas suggested things will need to move quickly if this deal is going to be completed:
United have made some smart acquisitions in the summer window so far in the form of Romelu Lukaku, Nemanja Matic and Victor Lindelof.
Getting in Sanchez, potentially from under the noses of their local rivals, would make a good summer a great one. However, it appears United will resist any temptation to get involved in a final-day scramble for the Arsenal star.