The French giants hope to mark their return to the top flight with several high-profile signings and they are keen on adding the England international to their ranks.
Lampard’s deal at Stamford Bridge is due to expire at the end of the season and everything suggests he will be leaving the Blues after 12 years at Stamford Bridge.
LA Galaxy are rumoured to be preparing a mega-money offer for the 34-year-old, but Monaco are not yet ready to give up just yet.
Lampard is still having second thoughts about Stamford Bridge stay, but with Chelsea officials yet to offer him a new deal, he seems to be edging closer to the summer exit.
The veteran midfielder will go down as one of the best players in club’s history, having scored more than 200 goals in official matches for the Blues.