The 31-year old has made just under 90 appearances in a four and a half year spell at Bolton but would relish the opportunity to move to the club whom he supported as a kid.
Barness was sent out on loan to the Hammers by Wanderers manager Sam Allardyce a year ago only to be recalled a 24 hours later due to an injury crisis at the Reebok Stadium.
This season the Londoner has been out of the first team picture and could be once again set to link up with Hammers boss Alan Pardew, his former Charlton Athletic team mate.
Wanderers have already seen the likes of Michael Bridges and Les Ferdinand depart the club in recent weeks thus paving the way for Allardyce to bring in some fresh faces.