The Evening Standard says the left-back could be heading to Stamford Bridge this winter.
Chilwell, 21, has established himself as one of the top defenders around after playing in all 38 of Leicester's league matches last season.
He's a vital cog in Brendan Rodgers' slick machine, with Leicester sitting SECOND in the table with eight wins from 12 games.
The Blues are currently appealing their two-window transfer ban at the Court of Arbitration for Sport, and will discover their fate in mid-December.
Should the ban be lifted, Lampard will be able to move for new players in January.