The Chile international is said to have been left angry and disillusioned by the 5-1 Champions League loss at Bayern Munich on Wednesday and reports claim he wants to move on when the season comes to a close.
Sanchez is due to fall out of contract in 2018 and is keen to depart as he enters the final year of his deal, with a host of sides from across Europe believed to be ready to make a move.
Manager Arsene Wenger has previously suggested the club could opt to keep hold of the former Barcelona attacker regardless of whether or not he signs a new deal.
However, with the Frenchman's future far from certain ahead of the end of his own deal coming to an end this summer it seems likely Arsenal will relent and allow Sanchez to move on at the end of the season.
Sanchez has been pictured in Italy in the wake of the defeat to Bayern, having been granted time off by the club, and Serie A pair AC Milan and Juvetus have both been credited with an interest.
Former side Barcelona have also been mooted as potential suitors and there is believed to be interest from Premier League leaders Chelsea - although it seems unlikely the Gunners will sell to a direct rival if that scenario can be avoided.