The Italian media claim that returning Chelsea boss Jose Mourinho has made an offer for the Napoli striker.
The fee is believed to be around £49.3million.
It’s also been reported that Mourinho has called Cavani personally in an attempt to persuade him to become his first major signing at the Bridge.
However, Cavani has a £53.6million buy-out clause in his contract and the Serie A club’s president Aurelio De Laurentiis has said he will not sell his star man for less than that figure.
De Laurentiis is now seeking to lure Real Madrid and Manchester City in to an auction, having already snubbed an offer from Chelsea of Fernando Torres plus £25.5million.