The Red Devils are expected to pursue a marquee striker and Gyokeres has been linked with a reunion with manager Ruben Amorim.
However, a transfer does not appear on the cards, considering the Swede wants to play Champions League football and fight for titles.
United are 13th in the English top-flight after 29 games. They won't qualify for the Champions League unless they win the Europa League.
Arsenal, elsewhere, are in a much better position. They are challenging at the top of the league and are almost guaranteed Champions League football.
The Gunners have a strong interest in the 25-year-old, who has netted a staggering 42 goals in all competitions for Sporting this term.
Gyokeres has a £85m release clause in his contract, but he has a gentleman's agreement to leave for around £60m this summer.