The Sweden international continued his excellent start to the 2024-25 campaign on Friday night, scoring four times in Sporting's 5-1 victory over Estrela Amadora, and he has now netted 20 times in 16 appearances this term.
Gyokeres has found the back of the net on 16 occasions in 10 Primeira Liga matches, while he has also managed two goals in three Champions League fixtures, netting against Lille and Sturm Graz in the competition this season.
Sporting head coach Ruben Amorim, who will officially take charge of Man United on November 11, allegedly wants to bring the 26-year-old with him to Old Trafford.
Gyokeres was asked about his future after scoring four times on Friday, and the Swede said that he is "really enjoying it" in Lisbon but did not rule out a move away from the club at the end of the current season.
Man United could target big-money Gyokeres move in 2025
"I don't know, I'm here. I really like being here, it's not something I think about. I'm enjoying it here," Gyokeres told Record.
Gyokeres has scored 63 goals and registered 19 assists in 66 appearances for Sporting since making the move to the Portuguese giants from Coventry City in the summer of 2023.
There is a €100m (£83m) release clause in his contract, although it has been claimed that he would be allowed to leave for around €70m (£58m) next year, and a number of clubs are said to be keen on him.
However, the imminent arrival of Amorim at Old Trafford has allegedly moved Man United to the head of the queue for a player who managed 43 goals in 116 games for Coventry ahead of his switch to Lisbon.
Ferdinand backs Amorim to move for Gyokeres
Former Man United defender Rio Ferdinand has backed the Red Devils to move for Gyokeres, claiming that the Red Devils could "break the bank" for the centre-forward.
"Gyokeres has scored a hat load of goals and Amorim has made a player out of him," Ferdinand told Rio Reacts. "I wouldn't be surprised if he says "there is one player I need to get out of there [Sporting] and it's going to be him.
"He's is integral for him. What happens to Rasmus Hojlund if they break the bank for someone like him? 64 appearances, 53 goals, played in England before albeit in the Championship. Would they break the bank for him and what would that mean for Hojlund? It's a big decision to make."
Hojlund made the move to Old Trafford from Atalanta BC in the summer of 2023, and the 21-year-old has managed 18 goals and two assists in 52 matches for Man United in all competitions.