Andersen joined the cash-strapped League One outfit on a short-term deal last month and has made six starts.
"I am counting on the deal being extended - I am very, very happy here," he said. "Even though Portsmouth are playing in League One it is still a huge club. There is a healthy mentality here and the fans are amazing.
"No matter where we play the fans will always be behind us. The home ground is almost always packed and sometimes when we play away from home the support is so great that it feels like a home game.