So far the signs are that Napoli, who are five points behind Serie A leaders Juventus and visit Parma on Sunday, will hold on to their talismanic striker, thanks partly to his 63 million euro buyout clause.
The powerful Uruguay striker, who scored his 100th Serie A goal in last Sunday's 1-1 draw at Fiorentina, has averaged more than one a game for Napoli in all competitions this season, making him one of European football's most prolific strikers.
Top scorer in Serie A with 17 goals, nine with his right foot, four with his left and four with his head, he has amassed 92 goals in just two-and-a-half seasons since joining Napoli from Palermo, making him the club's all-time sixth highest scorer.
He is closing in rapidly on Brazilian forward Careca (96) and Jose Altafini (97) and is only 23 short of Diego Maradona's 115, a total which took the Argentine seven seasons to reach.
"I have already received a 55 million bid for Cavani, and I said no," said club president Aurelio Di Laurentiis last week. "I need him, not the money."
"I trust in his professionalism. He knows that here he is the number one, while I believe that in other places or in teams he could not identify with the city, the shirt and the fans the way he does here."
Cavani also appeared to commit his future to Napoli after the Fiorentina match.
"I want to leave a mark on this city which has treated me fantastically. I'd like to give something special to our public," he said.
But with big-money clubs lurking on the sidelines, last-minute deals can never be ruled out.
Napoli fans, who saw forward Ezequiel Lavezzi depart for Paris St Germain in the close season, will only be able to breathe a collective sigh of relief when the deadline passes on Jan. 31.
As long as Cavani is still knocking in the goals, Napoli will have an outside chance of catching Juventus, who have looked more inconsistent and vulnerable than when they won the title unbeaten last season.
"There's nothing wrong with dreaming about the Scudetto, personally I am realistic and think we have to improve greatly but anything can happen in this championship," added Cavani
"In some matches, we have been lacking a bit of concentration. When you lack the will to win, you are at risk against any opponents. But we are improving in that aspect."
Roberto Donadoni's Parma will offer Napoli a stern test as they boast the only unbeaten home record in Serie A.
On Saturday, Leaders Juventus host lowly Genoa, who will be playing their first game under Davide Ballardini, their third coach of the season, after firing Luigi Delneri in the wake of their 2-0 home defeat by Catania.
Lazio, who have been a revelation having dropped only five home points, host an indifferent Chievo, who have lost eight of their ten away games.