The 34-year-old Chelsea legend could be set to leave Stamford Bridge at the end of the season - the England international is out of contract in June 2013 and is yet to be offered a new Chelsea deal - and the two Italian clubs are reportedly keen to bring him to Serie 'A'.
The report claims Lampard has been offered to Inter Milan, but a number of other clubs from across the world are thought to be interested in the midfielder.
Inter were believed to be keen to sign Lampard two seasons ago when Jose Mourinho was manager, but the England star opted to stay at Stamford Bridge.
But it now seems Chelsea are ready to let Lampard go on a free transfer at the end of the campaign. The former-West Ham playmaker scored both goals as Rafa Benitez's side beat Everton at Goodison Park on Sunday, underlining his ability to still make a difference in this talented Chelsea team.
The 34-year-old has been at Stamford Bridge for the past 11 years, winning three Premier League titles, four FA Cups and a Champions League with the Blues.
But that 11-year association looks increasingly likely to be coming to an end at the end of the season.