The Red Devils are bidding to sign a new central midfielder this summer, and Paris Saint-Germain's Manuel Ugarte is viewed as the club's leading target.
However, PSG are believed to be holding out for €70m (£58.9m) for the Uruguay international, and if the French champions refuse to drop their asking price, then Man United could be forced to look elsewhere.
Hjulmand was linked with Man United earlier this year, and according to FootballTransfers, the Red Devils are giving serious consideration to a move for the Denmark international this summer.
The 25-year-old was in strong form for his country at Euro 2024, with his standout moment coming in the group stage, when he scored a long-range goal against England.
Hjulmand 'back' on Man United's radar
The midfielder came through the youth system at Copenhagen, but he started his professional career with Admira Wacker before moving to Lecce in January 2021.
Strong form for the Italian outfit led to Sporting signing him in the summer of 2023, and the Dane was a vital player for the Portuguese giants last season, scoring four goals and registering four assists in 49 appearances.
Hjulmand has a contract with his Portuguese club until June 2028, but the deal includes a release clause of around €80m (£67.4m), which could be demanded in full.
As a result, Hjulmand may not be a cheaper option than Ugarte, and it is difficult to imagine the Red Devils being willing to pay more for the Dane when he is not considered to be their leading target.
Which other midfielders are being linked with Man United?
Real Sociedad's Martin Zubimendi, who helped Spain win Euro 2024, is said to be admired by Man United, with the midfielder potentially becoming an option this summer.
Adrien Rabiot is now available on a free transfer, meanwhile, and the Red Devils are believed to have a long-standing interest in the France international.
Youssouf Fofana of Monaco is another on Man United's radar, with the Frenchman likely to represent a cheaper option than both Ugarte and Hjulmand.
Man United have already allowed Donny van de Beek to depart this summer, but Casemiro, Scott McTominay and Christian Eriksen are also being linked with exits.
Hannibal Mejbri has travelled with the Red Devils on their pre-season tour of the United States, but the midfielder is not thought to be in head coach Erik ten Hag's plans for the 2024-25 campaign.