Madrid have made Paris Saint-Germain striker Kylian Mbappe their top target, though they need to raise funds via player sales.
United and Madrid are already in talks over the potential signing of defender Raphael Varane this summer.
And according to The Mirror, United have also been offered the Brazilian winger, with a loan move that turns into a permanent deal seen as the ‘most likely option’.
One stumbling clock for United though is that Real Madrid want a minimum of £68.5m for the 21-year-old.
United are already expected to announce the signing of Borussia Dortmund winger Jadon Sancho at any time, with a £73m deal agreed.
Vinicius is said to be disappointed that the LaLiga side are looking to move him on, given the fact that new manager Carlo Ancelotti hopes to keep him.
But Madrid are looking to raise around €150m (£128m) to sign Mbappe this summer despite his contract at PSG expiring next year.
Vinicius joined Madrid in the summer of 2018, a year after the club agreed a £36m deal to sign him from Brazilian side Flamengo.
Since his arrival at the Santiago Bernabeu, he has scored 15 goals in 118 appearances.