The center half has not been the subject of as much interest as the Blues would have hoped.
Chalobah, who is not wanted by the club, is a homegrown player whose sale would be a pure profit.
Per Sky Sports, West Ham are serious about the tall defender to replace Kurt Zouma.
The latter, who was a favorite of ex-boss David Moyes, could be heading to the Middle East.
West Ham have already paid big money for Wolves center half Max Kilman.