Forster is on loan at Celtic for the entirety of the 2019-2020 season.
There were some suggestions in Scotland that Southampton had a clause that would allow them to recall Forster.
But the 31-year-old has denied such reports.
Forster, who has played 15 games for Celtic this season, told reporters: "I don't think there's a recall [option], so I think I'm here for the season from my side of things.
"I'm happy here and glad to be back here playing.
"I just want to do as well as I can, so I think I'll be here for the season."
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