The centre half has been at The Hammers for the last three years after joining them from Spurs following a £1.1m move from Coventry City but has not played since last season after he was stabbed in the legs in an incident involving his sister and her boyfriend in Bedford back in August.
Davenport is back in training but with the cuts being introduced by West Ham's new owners, he is one of the players who will be allowed to leave.