First-team coach Fausto Salsano has admitted that City are interested in Slovakian midfielder Hamsik and Argentinian striker Lavezzi.
"Manchester City are watching Napoli very carefully. I can confirm Mancini's interest in Hamsik because I have been to watch the Slovak," Salsano told a Naples radio station.
"Marek has become a very important player with the right experience. Lavezzi, on the other hand, is a devastating player who can hurt you one-on-one. Hamsik and Lavezzi are players we like because our aim is to do great things."
Manchester City and Naples are currently in the same Champions League group.