Andersen joined the south-east London club from AB Copenhagen in a £721k deal during May 2004, and made his debut in the 4-0 defeat against Manchester United at The Valley a year later.
Despite starting last season as Athletic's first-choice keeper following an injury to Dean Kiely, 24-year-old Danish international Andersen has not been picked in the Addicks squad for any of the club's opening three fixtures.
New Charlton boss Iain Dowie has given the number-one jersey to new loan recruit and former Leeds stopper Scott Carson while Thomas Myhre has been on the bench.
That has allowed Andersen, who was recalled to the Denmark squad at the end of last season, to go out on loan, but the Addicks have insisted on the insertion of a recall clause.