The veteran goalkeeper has been on the search for a new club following his release from AC Milan in 2014.
He earned a trial with the Blues over the past month, following a long-term knee injury to first-choice shot-stopper Thibaut Courtois.
Blues boss Jose Mourinho has since then hinted that the 33-year-old could join the club on a short-term deal to act cover to Asmir Begovic for the number one role.
According to The Mail, the Premier League holders will confirm the signing of Amelia for a Bosman fee on Thursday.
It is thought that Amelia could feature in the club’s cup games as the Blues seek to provide ample rest to Begovic, who has been busy in goal since the start of the campaign.