The Red Devils have been tipped to make a move for the prolific 26-year-old following the arrival of new head coach Ruben Amorim from Sporting.
Amorim led his first training session as Man United boss on Monday ahead of his first game in charge away against Ipswich Town in the Premier League on Sunday.
The 39-year-old spent four-and-a-half years in charge of Sporting, winning two Primeira Liga titles and 71% of his 231 games across all competitions at the helm.
One of his standout performers over the last 18 months has been Swedish striker Gyokeres, who was signed by Sporting in the summer of 2023 for around £21m from Coventry City.
Man United send scout to watch Gyokeres
Gyokeres has since established himself as one of the deadliest strikers in Europe, scoring 66 goals and registering 19 assists in 68 appearances for Sporting across all tournaments.
The Stockholm-born striker has netted 23 of those goals in just 18 games so far this season, including 16 strikes in 11 Primeira Liga matches and a hat-trick in a 4-1 Champions League win over Manchester City earlier this month.
Gyokeres has also impressed on the international stage, scoring five goals in six UEFA Nations League games this year, and The Sun claims that Man United deployed a scout to watch the striker represent Sweden against Slovakia last weekend.
Sergio Souza - one of Man United's top Scandinavian talent spotters - is said to have watched Gyokeres in Stockholm score a third-minute opener in Sweden's 2-1 win over Slovakia in the Nations League.
Souza is said to have revealed his presence at the match via an Instagram video post during the national anthems.
Could Gyokeres join Man United?
Although Gyokeres has a contract at Sporting until the summer of 2028, his long-term future with the Portuguese giants is thought to be uncertain amidst the interest in his services from top European clubs.
The likes of Paris Saint-Germain, Bayern Munich and Arsenal have all been credited with an interest, but Amorim's move to Man United has seemingly put the Red Devils at the front of the queue for Gyokeres's signature.
Gyokeres recently refused to rule out the possibility of reuniting with Amorim at Man United, although he has insisted that he is yet to be contacted by his former coach since his move to Old Trafford.
Meanwhile, former Portugal international Jose Fonte believes that Sporting Lisbon may be forced to offload the striker - who has a €100m (£83.6m) release clause in his contract - due to financial constraints.