The keeper's contract is set to expire in the summer, and with the club so far failing to get him to agree on a new deal, they are consigned to losing him at some point.
That could be in January, with the Serie A side keen to at least get something for him rather than lose their man on a free in the summer.
That has alerted a number of club's across Europe, with the Blues reported to be among those that are monitoring the 32-year-old's situation.
Roberto Martinez's side have struggled in the goalkeeping department in recent seasons, with Tim Howard having come in for stern criticism from supporters.
Marchetti would then represent an attractive option to them, with him likely to be available cheaply in January or on a free in the summer.