Sanchez was subject to a number offers during the summer transfer window but a move never came to fruition.
Arsenal held off the advances of Manchester City who had a bid rejected on deadline day.
Arsene Wenger lined up Moanco’s Thomas Lemar as a replacement for the 28-year-old but he rejected the move to London.
Real Madrid have become the latest potential destination for the unsettled star and Spanish publication Diario Gol claim his representatives have already made contact with the Bernabeu hierarchy.
The Chile ace is into the final year of his contract at Arsenal so a January move could be on the cards if the Gunners want to recoup some of the £35m they paid in 2014.

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The speculation comes in light of Karim Benzema and Gareth Bale’s subpar performances this campaign and Real president Florentino Perez will now reportedly make a decision in the coming months.
Sanchez was prolific in what was a poor season for Arsenal last term scoring 30 goals in 51 appearances across all competitions.
The forward started, and notched a goal, against Cologne on Thursday night but was assigned to the bench for Arsenal’s trip to Chelsea on Sunday.