The Swedish striker has been in sensational form for the Lisbon-based club since signing from Coventry during the summer.
The 25-year-old has scored an impressive 17 goals in 20 games across all competitions and has quickly made a name for himself across Europe.
Chelsea have reportedly been keeping close tabs on the Swede as boss Maurico Pochettino eyes a new striker to help turn around his side's flailing fortunes.
But Gyokeres, who still has four-and-a-half years remaining on his deal, will likely command a sizeable fee from interested parties.
The 19-time capped Sweden international took just 11 minutes to break the deadlock in Monday's 2-0 win over Arsenal's Champions League round-of-16 opponents, FC Porto.
Read more on Chelsea
Newcastle eye little known rule that will allow Chelsea's own man to play against them
Mourinho clarifies De Bruyne and Salah Chelsea exits by telling critics they are wrong
Gyokeres collected the corner of the box before accelerating towards the touchline. He then produced a classy piece of footwork to pull away from the defender before aiming a superb low drive to beat the goalkeeper at his near post.
The win sees Sporting leapfrog city rivals Benfica into top spot heading into a two-week break from league fixtures.
However, Chelsea fans will be hoping Gyokeres will soon be packing his bags for an immediate return to English football.
Swathes of Blues supporters took to social media on Monday night requesting the club bring Gyokeres to Stamford Bridge to help fire Chelsea up the table.
Most read in Football
Ian Wright reveals real reason he is leaving Match of the Day
Former Tottenham boss candidate to replace under-fire Steve Cooper following shock talks
Van Dijk replies to Keane's arrogance claim after criticising Manchester United's tactics
Fulham to beat Man United, Liverpool and Arsenal to highly rated Brazilian in £20m+ deal
One fan wrote: "Come on Todd Boehly bring him to Chelsea."
A second fan added: "This man is special. Pay the fee and bring him to Chelsea. I'd hate to deter Sporting from winning the league though."
Jose Mourinho explains why Kevin de Bruyne and Mo Salah were sold by Chelsea when he was manager
A third wrote: "Bring him to Chelsea asap."
Chelsea fans appear to be prioritising a striker ahead of the January transfer window with Nicolas Jackson continuing to divide opinion.
Other names mentioned are Napoli striker Victor Osimhen and former academy star Dominic Solanke who is currently in fine form for Bournemouth.