Manchester United had scouts present to watch Martin Odegaard during Real Sociedad's La Liga fixture against Valencia at the weekend.
Since Real Madrid allowed the youngster to spend the campaign on loan at Sociedad, the 21-year-old has contributed four goals and five assists in Spain's top flight.
A report earlier this month claimed that Los Blancos plan to use the Norway international as a direct replacement for veteran Luka Modric next season.
However, according to El Diario Vasco, United are considering making a bid for the playmaker, a compatriot of manager Ole Gunnar Solskjaer.
The report says that United's head of global scouting Marcel Bout was in attendance to watch Odegaard feature in Sociedad's 3-0 victory over Valencia on Saturday.
Odegaard still has just under three-and-a-half years remaining on his Madrid contract.