Frank Lampard is a long-term admirer of the Leicester full-back, but the asking price – thought to be nearly £85million – meant the Blues may have looked elsewhere.
But the Evening Standard claims Chilwell is pushing through a move to Stamford Bridge, which could lead Leicester to drop their valuation.
The report suggests the Foxes may now accept a bid in the region of £50million for the 23-year-old, with Southampton’s Ryan Bertrand being lined up as his replacement.
Chelsea have already signed Hakim Ziyech and have all-but agreed a deal for the £53million transfer of RB Leipzig striker Timo Werner.
They are also thought to be near the front of the queue to sign Bayer Leverkusen star Kai Havertz, in what could be a summer of transfer business akin to the early Roman Abramovich days.
Lampard is reportedly willing to sell four Chelsea players to drum up the transfer fund for Chilwell.