The former Wycombe full-back has made over 75 appearances for the Bees since joining the club in 2010.
But Woodman, 29, has largely played second fiddle to Everton loanee Jake Bidwell this season and manager Uwe Rosler is ready to listen to offers for him.
"Craig is a competent League One left-back, who has shown his qualities over a number of years," Rosler told the Hounslow Chronicle.
"However, at the moment we can't give him the regular games that he needs.
"Both parties have agreed that if a club comes in and meets our valuation of the player then we are prepared to listen."