The Austrian has rejected the idea that the Englishman will be recalled in January.
Southampton are 18th in the Premier League but have three first-team goalkeepers in Angus Gunn, Alex McCarthy and Harry Lewis, the latter spent time on loan at Dundee United.
Hasenhuttl has backed Forster to stay with Celtic for the remainder of the campaign and get first-team football.
“First of all, I am very happy that he gets the chance to play after a long time," he 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.
"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."
Going forward it will be difficult for Celtic to sign the 31-year-old from the Premier League strugglers.
Contracted until 2022, he is set to pick up more than £7million in wages across that time.