The Uruguayan striker joined Paris Saint-Germain from Napoli last summer for €64m (£53m) but despite scoring 18 goals this season, the move has been seen as somewhat of a disappointment.
Cavani has had a couple of injury problems and has often been played wide as opposed to his favoured central striker position.
The 27-year-old signed a five-year contract at PSG but did admit in an interview with L'Equipe that his future could lie elsewhere.
"We'll see at the end of the season. We have to finish the season first," he said.
"I am in Paris, but there are certainly things we must talk about with the club, things should be done differently."
"Chelsea were interested," Cavani confirmed. " But the only thing that matters in the transfer window is spending money, just like Palermo did in 2009, Napoli in 2011 and PSG did last summer.
"PSG showed real desire and determination to include me in their project. When you see how much they invested in me, it is proof that they really want me.
"I do not know (if my agent has met with United and Chelsea). If something should happen, it's my brother who will do it and will be at the table with interested parties."
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- Paris Saint-Germain