The second part of Palmieri's medical is taking place at West ham.
Confirmation of the left-back's move to London is imminent after he agreed personal terms with the Hammers.
If the deal goes through, West Ham will take their spending this summer past the £120m mark.
He joined the Blues from AS Roma in January of last year, but has struggled to become a regular in the first team, often providing cover for Marcos Alonso or Ben Chilwell.
The 25-year-old left-back spent last season on loan at Lyon, where he played 29 league games and scored one goal, and will compete for the left-back spot with West Ham's 32-year-old left-back, which is currently occupied by 29-year-old
The transfer window will close at 11pm on September 1st.
Sky Sports has a dedicated Transfer Centre website where you can keep up-to-date with all the latest news. Sky Sports News gives you the ins, outs and analysis of sports.