The club remain in talks with full-back Billy Jones, who is out of contract in June.
West Brom director of football administration Richard Garlick said: "Chris and Graham have given the club long and valued service and played big parts in getting the team over the line last season.
"We have had ongoing discussions with Billy's representatives about a new contract since last October, when we offered him a new long-term deal with substantially-improved terms.
"Talks are continuing but they have proved fruitless so far as Billy has yet to put pen to paper."
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