French champions PSG have emerged as the favourites to sign Cavani and are understood to have already made a £43million offer for the striker.
However, Napoli president Aurelio De Laurentiis has been insistent that the Uruguay international will not be leaving the Serie A club for less than the €63m (£54m) buy-out clause in his contract.
Leonardo believes PSG's offer for Cavani is 'interesting' and he is hoping there will be some positive news on a potential deal in the next week.
"We presented De Laurentiis with an offer that I consider really interesting," Leonardo told Il Mattino.
"The negotiations continue. We will remain in contact and, in these next few days, there could be news."
Reports have claimed that Cavani, who is under contract at Napoli until 2017, has been offered a five-year deal by PSG worth €10m (£8.6m) per season.
Premier League duo Chelsea and Manchester City have also been heavily linked with Cavani, who finished last season as Serie A's top scorer.
Chelsea are understood to have made an approach to Napoli, but are not willing to meet the release clause in the 26-year-old's contract.
Cavani recently confirmed he is keen to discuss the situation with De Laurentiis after playing for Uruguay in the Confederations Cup in Brazil.
He has previously admitted it would be a 'dream' to play for Real Madrid and has also criticised Napoli's asking price.