The Chile international has been linked with a move away from the Gunners all summer after failing to agree a new deal at the Emirates.
Sanchez, who is said to have attracted interest from Manchester City and Paris Saint-Germain, has just one year remaining on his current deal, meaning that there is a chance that he could leave Arsenal for nothing next summer.
Rumours rumbled on social media that the 28-year-old had submitted a transfer request to force through a move elsewhere, but according to The Independent's football journalist Jack Pitt-Brooke, Arsenal have denied the reports.
Sanchez featured for the first time this season on Sunday when he played in 62 minutes of the Gunners' humiliating 4-0 defeat to Liverpool at Anfield.
Premier League clubs have until Thursday to complete their transfer business for the summer.