Gyokeres has been in red-hot form for Sporting during the 2024-25 campaign, scoring 23 goals in 17 appearances in all competitions, including seven goals in his last two matches against Estrela Amadora and Manchester City.
The Sweden international struck a hat trick against Man City in the Champions League on Tuesday night, and he is believed to be on Man United's radar, with Amorim set to swap clubs on November 11.
Amorim refused to reveal whether his new team could move for the 26-year-old, but he did suggest that a departure for the centre-forward at the end of the current season is on the cards.
"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."
Man United 'could move for Gyokeres next summer'
Gyokeres has scored 66 times and registered 19 assists in 67 matches for Sporting, and there have recently been claims that he could be allowed to leave next summer for €70m (£58m) despite having a €100m (£83m) release clause in his contract.
"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 when asked about his future following Sporting's last league match against Estrela.
Ex-Man United captain Rio Ferdinand has claimed that the forward could be Amorim's "number one target" at Old Trafford and also discussed the Swede's unusual journey to the top of European football.
Gyokeres was contracted to Brighton & Hove Albion between 2018 and 2021, but he only made eight appearances for the club, spending time out on loan with St Pauli, Swansea City and Coventry City before eventually completing a permanent move to the latter.
Ferdinand talks-up potential Man United move for Gyokeres
"The recruitment teams in all the clubs in the Premier League must be scratching their heads about how they let him get away," Ferdinand told TNT Sports.
"He hasn't had a conventional route, his route to the top hasn't been straightforward. He was at Brighton as a kid, sold to Coventry, went on loan to Swansea, goes back to Coventry and does well, then goes to Sporting Lisbon.
"He has had a journey where he has had to build himself and create what he is now. You think 'How has he been allowed to get out?', all of a sudden when are seeing what he has got, maybe he has grown into what he is, the confidence, stature he has, the physicality, he might have had to wait for that to come. A few times today he blew away from players, holding people off.
"It's going to be interesting. Managers want to leave clubs and there's always one or two players where they're thinking that guy knows how I play. Everyone can feed off him maybe.
"Who is that guy going to be? If he's going to take someone from Sporting, after the way this guy has been playing in the last few weeks, 11 [goals] in five games, is he going to be the number one target for the new manager at Man United?"
Amorim's final match in charge of Sporting will come against Braga on Sunday night, while his first game as Man United head coach will be the team's Premier League clash with Ipswich Town on November 24.