The 24-year-old subsequently gave Chelsea sufficient encouragement to trigger his release clause, believed to be €55 million (£49.4m). Chelsea have offered a five-year deal worth £200,000-a-week.
Werner is yet to sign the contract but has agreed terms and, barring an 11-hour intervention by another club, will join Chelsea next week.
Having already secured the signature of Hakim Ziyech from Ajax, Frank Lampard's remodelling of the club is beginning to take shape.
As ESPN reported, Lampard is an admirer of Chilwell and wants to overhaul his options at left-back this summer. Both Marcos Alonso and Emerson Palmieri will be free to leave the club and Chilwell's emergence at Leicester has put him at the top of Chelsea's wishlist.
The Blues enquired about Chilwell's availability prior to the January window but were told he was not for sale. Chilwell has not agitated to leave but he is thought to be interested in joining Chelsea.
However, Leicester are in a strong position to drive a hard bargain given he is under contract until 2024. They are also more financially robust than some clubs feeling the effects of the coronavirus pandemic.
Ajax's Nicolas Tagliafico and Porto's Alex Telles are viewed as cheaper alternatives if no agreement can be struck but Chelsea are hopeful of being able to land Chilwell despite Leicester's valuation standing in excess of £70m.