The Uruguayan international moved to the French outfit from Napoli last summer, but has reportedly become increasingly frustrated with life in Paris.
Zlatan Ibrahimovic's presence has meant that Cavani has been deployed in a wide area this season, but the 27-year-old has still scored 22 times in 37 games.
"Edinson believes he will be a perfect fit in England. He knows that United, Manchester City and Chelsea are all interested and would be happy to talk to any of them. But he also knows United seem the most keen and that is a factor," The Mirror quotes a source as saying.
It is understood that United's absence from the Champions League next season is not an issue for the forward, who will travel to the World Cup with his country this summer.