The 34-year-old midfielder is yet to be offered a new contract to extend his stay at Stamford Bridge, and so will be a free agent at the end of the season.
The Serie 'A' club are keen to bring the England international to Naples, and are willing to make an audacious bid for the Chelsea legend's signature.
Lampard received numerous offers during the January transfer window - including one from MLS side LA Galaxy - but opted to remain in west London for the rest of the 2012/13 campaign.
Currently three goals shy of Bobby Tambling's all-time record of 202 Chelsea goals, Lampard will be determined to surpass that milestone before calling time on his decorated Blues career.
The box-to-box midfielder is also one of only seven players - and the only midfielder - to have scored more than 150 goals in the Premier League, and played an instrumental part in Chelsea's back-to-back title winning campaigns in 2004/05 and 2005/06, and the club's domestic cup double in 2006/07.
Lampard also captained Chelsea to their first Champions League crown last season, after a penalty shootout victory over Bayern Munich at the Allianz Arena last May.
And, with Napoli currently occupying second place in the Serie 'A' table, their expected qualification for Europe's elite club competition next season could play a pivotal part in securing Lampard's signature.