Lampard, 34, will quit Chelsea in the summer according to new interim manager Rafa Benitez and Ranieri, who bought Lampard from West Ham United for £11 million in 2001, wants to take advantage of Lampard's lack of first team football with the Blues.
The England international, who won three Premier League titles with Chelsea, is set to depart Stamford Bridge after 12 years at the club.
Chelsea are already looking to sign a replacement for Lampard with Corinthians midfielder Paulinho and Everton midfielder Marouane Fellaini on their radar.
Lampard has played 574 games for the Blues with 189 goals and is third highest goal-scorer at the club. Being a midfielder, Lampard is the only player to have scored over 150 goals in the Premier League.
The 34-year-old has 93 caps with England scoring 26 goals.