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Gyokeres netted an impressive 43 goals in 50 appearances, playing a key role in Sporting's Primeira Liga title win last season.
The forward only arrived in Portugal a year ago from Championship side Coventry City but is already being tipped for another move.
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Transfer guru Fabrizio Romano has claimed that Arsenal is readying an initial offer for Gyokeres, estimated to be between £55 million ($70.1 million) and £60million ($77.5 million).
Chelsea is also named in the report as having an interest in signing Gyokeres, who has been identified as a target and an alternative to Napoli's Victor Osimhen.
Talk surrounding Gyokeres' future began to intensify earlier this summer after his impressive season in Portugal.
After helping Sporting clinch the league title in Portugal, the striker discussed his future amid speculation that he could depart the club this summer.
"It's football, I can't promise anything, I have a contract and I won't be sad if I stay," Gyokeres told Bola Na Rede back in May following the conclusion of last season.
We can't predict much, but let's see what next year will be like, we still have games this season."
Liverpool.com says: Gyokeres would be a risky transfer for any top Premier League team to complete.
Although he scored 43 goals last season, it's only been a year since he was a Championship player.
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