Roberto Mancini has assembled a list of transfer targets and will be looking for more backing from the new City directors above him than he received from Brian Marwood last summer.
Cavani is expected to leave Naples with the Serie A club already looking at Sampdoria's prolific teenage striker Mauro Icardi as his replacement.
Mancini has previously spoken about his admiration for the Uruguayan, who almost single-handedly put City out of the Champions League last season with crucial goals in both home and away games between the clubs.
Cavani, 25, has scored 18 goals in Serie A this season and is also being targeted by Real Madrid with reports in Spain today claiming that the Bernabeu club are ready to offer 50million euros and a player in part-exchange.
Paris Saint-Germain and Chelsea are backing off from the auction and may fight it out for Radamel Falcao instead.
City's interest in Varane, 19, the Real Madrd centre-back who was outstanding against Barcelona last week, also appears to signal that Joleon Lescott could be surplus to requirements at the end of the season.