Gyokeres is believed to have become Man United's leading centre-forward target for next summer's transfer window following the departure of Ruben Amorim to Old Trafford as the new head coach.
Amorim managed Sporting on 231 occasions between March 4, 2020 and November 10, 2024 before taking charge of Man United, with the 39-year-old's arriving in England at the start of last week.
There is currently a host of speculation surrounding Gyokeres's future, with Amorim admitting towards the end of his time at Sporting that the Sweden international is likely to be on the move next summer.
Arsenal, Manchester City and Barcelona are among the clubs said to be keen on the 26-year-old, but the Amorim link is believed to have placed Man United firmly at the head of the queue.
Gyokeres responded "we'll see" when asked about Man United interest
"He has of course meant a lot [to me] considering that he gave me that chance and that he made me develop so much," Gyokeres told Fotbollskanalen when asked about Amorim.
Gyokeres was then asked directly about a move to Man United, and he revealed that he had not yet been contacted over a potential move to the 20-time English champions.
"He [Amorim] probably has some strikers there already, so we'll see. No, he hasn't [contacted me]. It's fun but nothing I attach any importance to because it's talk and nothing concrete," he added.
Gyokeres was also asked what he would require from a new club, and he responded: "That you get an important role and that you get to play. That's the most important thing. There are other things that also need to be in place, but I'll take it when it comes."
Will Man United move for Gyokeres next year?
The forward has a €100m (£83m) release clause in his contract, but it is understood that he will be allowed to leave the Green and Whites next summer for a fee in the region of €76m (£63m).
Man United's senior strikers Rasmus Hojlund and Joshua Zirkzee have only scored three goals between them this season, and the Red Devils are expected to be in the market for a new forward in 2025.
Gyokeres is a goal machine, scoring 23 times in 18 appearances in all competitions at club level this term, while he has 66 goals in 68 appearances for the Lisbon giants in all competitions since arriving from Coventry City in 2023.
The forward starred under Amorim at Sporting, and a lot of the signs are pointing towards a reunion in Manchester.
A move for Gyokeres to Old Trafford could spell the end of Zirkzee's time at the club, with the Netherlands international likely to depart next summer if he continues to struggle to make his mark.