The Swedish forward has been on the radar of several top European clubs.
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Gyokeres, who has a €100 million release clause, has scored more than 50 goals for Sporting since joining at the start of last term.
According to HITC, he may be ready to call time on his career in Portugal very soon.
Even a winter move is a possibility, as he wants to play for a club challenging for elite titles.
Competing in the Premier League and Champions League with Arsenal may be too good a chance to turn down.