Cavani joined PSG from Napoli last summer, signing a five-year contract after joining them in a £55million deal.
But according to the Daily Star, the Uruguay international is interested in a move to the Premier League and United are ready to launch a bid for the forward this summer.
Reports in Italy this week have also suggested that United could move for Cavani at the end of the season, although PSG are highly likely to do everything they can to keep hold of the player.
United's reported interest in Cavani comes as Wayne Rooney continues to be linked with a move away from Old Trafford.
Rooney will enter the final year of his contract at the end of the season and continues to be linked with Chelsea, as well as PSG and Real Madrid.
Earlier this week, David Moyes claimed "big players" still want to join Manchester United as they remain the biggest club on the planet.
Moyes has been told that he will receive all the financial support he needs as he looks to strengthen his squad and overcome a poor first half in his first season in charge of United.
The Red Devils' chances of successfully defending their Premier League title are all but over, and United face a battle to secure a top-four finish.
However, Moyes remains convinced that he made the right choice in agreeing to succeed Sir Alex Ferguson last summer.
"Manchester United are not only the biggest club in this country, but the biggest club in the world," he said prior to Sunday's 3-1 defeat at Chelsea.
"I don't think any of the aura is fading whatsoever. Some of the results have not been what you would want, but I wouldn't say the aura is fading - in fact, I think the opposite.
"There is no issue about signing big players - not by my trips and the things I am hearing.
"The number of big players wanting to join Manchester United is incredible.
"Maybe players want to go to other clubs for the money, but if you ask them where they really want to be, which club they really want to wear the badge of, they want to wear the badge of Manchester United.
"It's because of what this club stands for in world terms - everything about it.
"The share price doesn't matter whatsoever. Players are not looking at the share price. What they are looking at is the club and what it stands for in football and world terms.
"It is renowned throughout the world, wherever you go, and I don't see that changing."