Ashdown, who spent most of the season as understudy to Marcus Hahnemann, was rushed into the first team after an injury to Hahnemann and excelled as he kept his side in the team up to the finish of the season.
However, Ashdown has rejected a new contract at the Madejski Stadium and is rumoured to be in talks with Portsmouth.
Portsmouth are light on keepers, with Pavel Srnicek leaving for West Ham mid-season, Chris Tardif being released and now Herald Wapennar confessing he would like to exit Fratton Park.
Meanwhile, midfielder Carl Robinson is expected to complete his transfer to First Division Sunderland within the next few days.