Gyokeres has emerged as a potential target for a number of European clubs, having been in scintillating form since joining Sporting from Coventry City last summer.
The striker has racked up 36 goals and 14 assists in 39 competitive appearances for Ruben Amorim's side this season.
Having scored 22 of those goals in 24 league games, the Sweden international is currently leading the scoring charts in the Portuguese top flight.
Arsenal are believed to be among the clubs to have taken a keen interest in the Sporting man, and they have supposedly earmarked him as a leading forward target for the summer transfer window.
However, the Gunners could face competition from their Premier League rivals Chelsea, who have also been linked with the former Coventry man.
According to the Daily Mail, Chelsea sent scouts to keep a close eye on Gyokeres in Sweden's 5-2 friendly defeat to Portugal on Thursday.
The Chelsea representatives saw Roberto Martinez's side establish a four-goal lead, before Gyokeres found the net in the 58th minute.
The 25-year-old tapped the ball home from Emil Holm's driven pass to register his sixth goal in 20 international appearances.
After Goncalo Ramos added a fifth for Portugal, Gyokeres was replaced by Gustaf Nilsson, who netted a late second in Jon Dahl Tomasson's first game as Sweden boss.
While Gyokeres has a contract with Sporting until the summer of 2028, his deal is believed to contain a €100m (£85.5m) release clause.
The prolific marksman recently insisted he is under "no stress" despite being linked with a move away from his current employers.
Chelsea are believed to be on the lookout for a new number nine, having been left unconvinced by Nicolas Jackson's first season at Stamford Bridge.
The former Villarreal forward may have scored in Chelsea's last two Premier League games, but he has struggled to find consistency in the final third this season.