The Red Devils have long been linked with the Uruguayan international, with some speculation having hinted that he was unhappy at Paris Saint-Germain.
However, the 27-year-old would only consider a switch to Old Trafford if United were in Europe's top club competition, according to the Daily Mail.
As it stands, that appears to be unlikely, with David Moyes's team seventh in the Premier League and some 12 points adrift of fourth-placed Manchester City, who also have two games in hand on their rivals.
They could also secure their place in the tournament by winning this season's version, but that would first mean overturning a 2-0 deficit against Olympiacos tomorrow night, before potentially having to see off the likes of Bayern Munich, Barcelona and Real Madrid from the quarter-finals onwards.
The lure of Champions League football was believed to have been one of the major motivating factors behind Cavani's decision to swap Napoli for PSG last summer.