After a tough start to Premier League life, the Saints seem to have acclimatised to top-flight football, epitomised by an impressive 1-1 draw with Arsenal on Tuesday.
And Adkins has vowed to stand by his keepers - Kelvin Davies, Paulo Gazzaniga and Artur Boruc - despite all three having made notable errors.
The Saints boss, himself a former keeper, said: "We have a young goalkeeper in Paulo Gazzaniga, who is going to be the future of this football club.
"We have two experienced goalkeepers in Kelvin Davis and Artur Boruc.
"They are the three goalkeepers we've got now and I do not anticipate another goalkeeper coming in during this window."
Adkins is still looking to strengthen his squad in the January transfer window, with Cagliari defender Davide Astori among those linked with a move to St Mary's.
"I think you've always got to improve," Adkins said.
"You can't stand still. Whatever we've done in the past is in the past. We've got to keep looking at the future.
"We've got to keep moving forward, moving on and everyone has got to keep striving to do that.
"We've had our recruitment meeting well before the January window has opened.
"We have a good recruitment department, we have targeted several players, we have had conversations about availability and non-availability.
"I would like to think that during the course of the window a couple of people will be coming in."
Adkins also expects a number of squad players to leave for pastures new, but esteemed teenager Luke Shaw will not be among them.
He added: "As I have said before, Luke is better playing for Southampton Football Club, where he is being nurtured and looked after.
"He is still only 17 and playing in the Premier League, where he is getting an opportunity to flourish, to make some mistakes and to keep kicking on.
"We have a good culture here. He is under contract, we are not looking to let him go.
"This is best place for him at this point in his career. He has a big, big future in the game, which he demonstrated with his performance against Arsenal the other night.
"If anyone wants to try and do business, all the best dealing with the chairman."