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The Chilean winger had been widely expected to link up with Pep Guardiola at the Etihad Stadium this summer, but the Gunners are steadfastly refusing to strengthen a domestic rival.
According to the Daily Mail, Arsene Wenger is still hoping to tie Sanchez down to a new long-term contract but is losing faith in his ability to convince the forward to extend his stay in north London.
And if Sanchez refuses to sign a new contract, Wenger has made it plainly clear that he will not entertain any offers from English clubs, thus making him choose between renewing with the Gunners or leaving his home in England.
It is a dangerous game to play, with Sanchez’s current contract expiring in 2018, meaning he can begin negotiating a free transfer in January.
The two European clubs best placed to sign the 28-year-old are Bayern Munich and Juventus, though both sides are likely to offer cut-price fees given that Sanchez’s contract expires so soon.
Both Man City and Chelsea – who held positive talks with the player’s camp – were believed to be willing to offer in excess of £45 million, but Bayern and Juve will not offer anything close to that.