Maurizio Sarri is keen on the Uruguayan who was the most expensive signing in French history when he moved to PSG from Napoli six years ago.
Sarri who is preparing to remodel his squad in the next two transfer windows could offload six or seven players this month alone.
He has seen his side only score 38 goals in the Premier League which is comfortably the lowest number of the clubs in the top six and has lost faith in his front men.
Cavani, 31, has scored 324 goals in 519 appearances could be the right man to get his side firing in goals again but they could find they have competition from China.
Meanwhile the Blues are also interested in finalising a deal that will see them pay £45million for Cagliari’s Italian international midfielder Nicolo Barella.
Like they did with Christian Pulisic Chelsea will agree a deal for Barella, 21, seen as one of the best talents in Italy now and he will then move to Stamford Bridge in the summer.
The Blues are also set to let Cesc Fabregas leave the club this month.
The Spaniard bid an emotional farewell to Stamford Bridge on Saturday in the 2-0 FA Cup win over Nottingham Forest.
Speaking after what is believed to be his final Chelsea appearance, Fabregas admitted: “The occasion got the better of me.
“I didn’t expect all of this to happen today.
“I can’t say anything out of respect for Chelsea but everyone knows the situation.”
Fabregas is expected to link up with his former Arsenal team-mate Thierry Henry who is now the manager of Monaco.
The Ligue 1 side are second from bottom and desperate to avoid relegation.
Chelsea return to action on Tuesday when they take on Tottenham in the first leg of their Carabao Cup semi-final.