The Italian coached the midfielder during his time at the Premier League club, and is thought to still be a huge fan.
With the 34-year-old’s current contract situation, Ranieri believes that he could be able to tempt the England international to complete a sensational switch to the second tier of French football.
Lampard is said to be keen to renew his deal at Stamford Bridge, but the club’s owner Roman Abramovich is looking to axe a number of aging players during the next few transfer windows.
It’s believed that he has told the club’s vice-captain that he will not be offered a new contract.
Monaco would be unable to match ex-West Ham man’s £130,000-per-week wage, but could offer him a similar income due to the tax rules in the principality.
The Mediterranean club are thought to be willing to make a January move, but it is unclear as to whether Chelsea would demand a significant transfer fee.
If they do, then the Stade Louis II side would return at the end of the season, once his contract has expired.
Lampard has spent 12 years in West London, winning three Premier League titles and four FA Cups.