Both players have been on the radar of the Premier League pair but a move to England has now been effectively ruled out with Lavezzi on the verge of a move to French club Paris Saint German and Cavani deciding to remain in Naples.
Argentine playmaker Lavezzi is wanted by champions City with manager Roberto Mancini seeing him as the perfect foil for fellow South American Sergio Aguero next season.
However the 27-year-old is close to signing for mega rich PSG although admits that he is in the dark about the finer details of his move to the Parc de Princes with the deal yet to be fully completed.
“I don’t know a lot of details,” Lavezzi told Il Mattino. “Negotiations are being managed by my agent.
“Naples will always hold a special place in my heart and I have great affection for the people.
“Napoli launched me and gave me a lot of international visibility.”
Uruguay international Cavani has also stated his intention to remain with Napoli despite speculation linking him with a move to Chelsea and Scudetto winners Juventus.
His haul of 23 goals in 35 games last season was instrumental as the azzurri outfit secured a fifth-place finish and last months Coppa Italia triumph – their first silverware in 22-years.
“I know nothing about Juventus,” Cavani said to Corriere dello Sport. “I want to stay at Napoli.”
Blues owner Roman Abramovich is a known admirer of the 25-year-old forward and targeted him to fill the void left by Didier Drogba but could be put off by his desire to remain
The Russian billionaire is still trying to broker a deal for Porto striker Hulk but wanted Cavani to form a devastating strike force with the Brazilian that would fire the West London club back into the top four.