The London Evening Standard says Mourinho is a huge admirer of Cavani, who has told his agent to look for a move away from Paris Saint Germain.
Chelsea tried to buy Cavani last year before he joined the French champions for £55m but his large transfer fee and wage demands could be an issue.
It comes despite Cavani insisting today that he is happy in Paris.
"I am sure to stay, why would I not?" he told L'Equipe while with PSG in Beijing.
"I'm well in Paris. I have a contract to honour. I'm calm, I'd rather be here. I feel good here. However, I know it does not depend solely on the player but also on the club," he admitted.
The club would also need to offload two foreign players before bringing another one in to meet the Champions League and Premier League quota.
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