ESPN says there'll be no move this month, instead the Gunners are sounding out the former Manchester City striker about a Premier League return this summer.
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Key to the deal will be Arsenal sports chief Andrea Berta, who signed Alvarez for Atletico two years ago.
Atletico are willing to sell, but are insisting on a €100m valuation.
For their part, Arsenal management concede they still lack options in attack, despite Viktor Gyokeres' arrival last summer and Gabriel Jesus' return to fitness and form.
Arsenal are now in contact with Atletico and have asked to be kept up-to-date on Alvarez's situation leading up to the summer market.