The Sweden international was heavily linked with a move to the Premier League over the summer following a magnificent 2023-24 debut campaign for Sporting, after leaving Coventry City in July last year.
Gyokeres scored 43 goals and registered 15 assists in 50 appearances for Sporting across all competitions last season to help the Portuguese giants win the Primeira Liga title.
The 26-year-old has since made an impressive start to the new campaign, netting seven goals in just four top-flight matches as Sporting sit pretty at the top of the table with a maximum 12 points.
Earlier in the summer, it was reported that Arsenal scouts were 'very impressed' with Gyokeres after watching him in action for Sporting last season.
Gyokeres content at Sporting amid PL interest
Despite being in the market for a new centre-forward, Mikel Arteta's side opted against meeting Gyokeres's €100m (£85m) release clause and instead swooped for wide forward Raheem Sterling on loan from Chelsea.
Enzo Maresca's side were also on the lookout for a new striker, but they were unable to get a deal over the line for any of their top targets, including Gyokeres, Victor Osimhen, Ivan Toney and Jhon Duran.
Gyokeres recently admitted that he has "absolutely no problem" staying at Sporting, but he refused to rule out an exit in future transfer windows.
The striker has also revealed that he 'wants to play at the highest level', suggesting that a future move to the Premier League is something he would be interested in.
Gyokeres to stay at Sporting in January?
However, according to Football Insider, Gyokeres may be reluctant to leave Sporting in January, midway through the season, as he is currently settled in Portugal.
The report adds that Gyokeres could even reject a winter-window move to clubs such as Arsenal, unless they were to activate his release clause.
It is understood that Premier League clubs including Liverpool, Manchester United and Tottenham Hotspur are also keeping tabs on Gyokeres and could rival both Arsenal and Chelsea for his signature in the next 12 months.
Gyokeres, who still has four years remaining on his contract at Sporting, impressed for Sweden during the international break, contributing with three goals and two assists in UEFA Nations League victories over Azerbaijan and Estonia.