According to talkSPORT, the Napoli forward mentioned Barcelona and Real Madrid as potential destinations, while admitting he's unsure of his future while still contracted to the Serie 'A' club.
Chelsea and City have been linked with the former-Palermo striker, with Roman Abramovich reportedly eager to avoid missing out on another top striker following reports of Radamel Falcao's imminent move to Monaco.
But the Serie 'A' top scorer has dampened talk of a Premier League switch, revealing it's been one of his long-term ambitions to play in the Spanish top flight.
"As a child I dreamed of playing for Real Madrid or Barcelona, but now I am proud to be at Napoli, this is important," Cavani said.
"On my future I cannot say anything, because I still do not know anything.
"I do not get distracted at all when I hear about offers and interest from other teams, I am used to it now. Honestly, I still have a contract and I just think about Napoli."
Barcelona have agreed a deal to bring Neymar to the Nou Camp, while Real Madrid have been linked with a move for Spurs star Gareth Bale.
Both Manchester City and Chelsea are thought to be on the lookout for a new striker, as they look to mount a title challenge to Manchester United next season.