Gyokeres has scored 66 times in 67 appearances for Sporting, including 23 goals in 17 outings in all competitions this season, and he is believed to be firmly on Manchester United's radar for next summer.
Ruben Amorim is leaving his role as Sporting manager to become Man United's new head coach, and there has been intense speculation surrounding Gyokeres' future since the move was confirmed.
The Sweden international scored a hat trick against Manchester City in the Champions League on Tuesday night, and after the European clash, Amorim said that the striker would likely be on the move next summer.
"If I start joking about this Gyokeres situation I'll get in trouble," Amorim told reporters. "This is my city, this is my country, so I'll respect it. Viktor has to stay until the end of the season and then his life will probably go somewhere else."
Gyokeres 'could leave Sporting for €76m (£63m)'
According to The Sun, there is a gentleman's agreement between Gyokeres and Sporting that would allow him to leave the club for a fee in the region of €76m (£63m) during next summer's transfer window.
The report claims that Arsenal and Chelsea are also keeping a close eye on the situation, with the London pair expected to be in the race for his signature next year if it becomes clear that he will be leaving Lisbon.
Gyokeres was asked about a possible move to Man United after scoring four times for Sporting against Estrela Amadora on Friday night, and he told Record: "I don't know, I'm here. I really like being here, it's not something I think about. I'm enjoying it here."
The 26-year-old has scored five times in four Champions League appearances this season, and he would likely become Man United's starting striker ahead of Rasmus Hojlund if he moved to Old Trafford.
Hojlund continues to face criticism despite boasting a respectable tally of 18 goals in 50 matches for Man United, and the Denmark international has been backed by the club's interim head coach Ruud van Nistelrooy.
Van Nistelrooy defends Hojlund amid criticism
"My advice? Stay calm and believe in himself, believes in his qualities. Like I do and his teammates do. He knows he's young and he's promising and the daily work he puts in will pay off in the end. Not only for him but his teammates," said Van Nistelrooy on Wednesday during a press conference when asked what advice he would offer to Hojlund.
"And I'm confident in that. I mean, most goals are scored in the penalty area, it's where we want to get our players as much as we can, but it depends on the games. There have been games where we've arrived many, many times, creating many chances. Unfortunately, we couldn't convert them all and that cost us a couple of results.
"But you have to deal with circumstances. When it's needed, to hold up play and get players into the third-man position and play on from there, he does a brilliant job [with that] as well.
"And, of course, he is a guy who can change a game in a second, like with the penalty moment [against Chelsea]. We just need one or two in the box, and you can be him but it can be the others as well, so that's a threat we always have."
Hojlund has only managed two goals in 10 appearances for the 20-time English champions during the 2024-25 campaign, with just one of those coming in the Premier League.