Pellegrini is expected to be confirmed as Roberto Mancini's replacement at the Etihad Stadium, and he could also bring with him the highly-regarded £27m-rated Isco.
The Spaniard has a release clause in his contract to the value of £27m, while Cavani has a similar buyout clause in his Napoli contract that allows him to leave for £52m.
The Serie 'A' side will not let him leave for anything less than his release clause though, so City could be set to splash out up to £80m on the two players.
The Daily Mirror quotes sources that claim a deal for Cavani is close to being finalised, while Isco more closely depends on the arrival of Pellegrini.
Mancini's City team lost the FA Cup final to Wigan on Saturday, but reports suggest the Italian was set to be fired regardless of the result at Wembley Stadium.
Most reports have Pellegrini as the favourite to succeed Mancini, but the Malaga coach insisted on Monday morning that a deal has not been reached to bring him to the Premier League.
Mancini criticised the City board for a failure to act early and decisively in the transfer market last summer, and they look confident of avoiding the same mistake again this term.
An Abu Dhabi source told the Daily Mirror: "All the talk here is not just about Pellegrini, but also that City think they've got Isco and Cavani.
"They seem very confident and very excited about it. Things are obviously happening very quickly behind the scenes."
Edin Dzeko has been mentioned as a possible makeweight in a deal for Cavani, but the Bosnian international is thought to prefer a return to the Bundesliga - with Borussia Dortmund reportedly interested.