The 31-year-old has impressed at Celtic Park after moving back for another stint during the summer.
Forster saved a penalty to help Celtic beat Rangers in the Betfred Cup final at Hampden Park on Sunday.
"First of all I am very happy that he gets the chance to play after a long time", Hasenhuttl said.
"That he is a fantastic goalkeeper, I always knew, but for him it was important to get the chance to play and to get the games and self confidence back. I am very happy for him."
Hasenhuttl was pressed on whether Forster, who is contracted until the summer of 2022, could be set for an early recall.
The Southampton manager said at a press conference: "We have our two goalkeepers, or three goalkeepers, here, and he is on loan until the end of the season. It is not the moment to think about that."