The 26-year-old Napoli striker is a reported target for the Barclays Premier League club, who have reinstated Mourinho at Stamford Bridge after a six-year absence, while English runners-up Manchester City have also been linked with an approach for Serie A's top scorer.
Cavani is among the most highly-rated strikers in Europe having hit 29 goals for Napoli in the 2012-13 season and, despite being under contract at the Stadio San Paolo until 2017, he confessed he would enjoy linking up with Portuguese Mourinho in London.
The Uruguayan would also consider collaborating with Chilean tactician Manuel Pellegrini, who claims to have a verbal agreement in place to become City's next manager.
Speaking at Uruguay's pre-Confederations Cup retreat in Brazil, he told Sky Sports News: "The Special One? It would be a pleasure to be managed by someone like him.
"Chelsea? I don't know if they've made an offer for me but I know that working for a coach like Pellegrini or Mourinho would be a great pleasure.
"It would certainly be a great honour to join one of the illustrious teams that are looking at me because I dreamed about doing that as a child.
"At the moment, though, I am only focused on Uruguay."
Cavani will definitely make a connection with a one-time Chelsea boss when he returns for pre-season training with Napoli, given Rafael Benitez has agreed to take control at San Paolo from the beginning of July.
The Spaniard spent seven months as interim boss in west London and his first task will be trying to persuade the prolific Uruguayan to prolong his three-year stint in Naples.
"I don't know if Benitez's arrival could affect my future," Cavani added. "Today [Monday] I have a contract with Napoli but, at the same time, I'm talking to other teams.
"Things are bit uncertain at the moment. The only certain thing is that I belong to Napoli and I'm concentrating on Uruguay because we have a tough tournament like the Confederations Cup.
"After these engagements I will think about my future.
"I'm relaxed at the moment because I've endured rumours about having signed for other teams throughout my career, when it hasn't been true.
"People talk about big sums of money, about sales, about loan moves, and I'm used to it. I know that people like talking about big numbers but I have to stay honest and focus on the present.
"There are other things than football. I'm staying down to earth, happy, and relaxed and we will see what happens."