Stekelenburg missed out on playing in the Saints' most recent fixture against Leicester City, after suffering with a back complaint, but he is set to start on Sunday.
“He’s looking good,” Koeman confirmed. “He did Thursday, on a day off, a session with Dave Watson.
“He was training normally on Friday and he’s fit for the weekend.”
Stekelenburg's return to health is a major boost for Southampton, who could ill-afford to be without their two best goalkeepers for much longer, with Fraser Forster also out for the long-term.
Kelvin Davis did an admirable job stepping into the team, but he is ageing now and Stekelenburg is a much more secure option between the sticks for Koeman's side.
Unfortunately for the south coast outfit, their fitness update was no all positive, with a number of players set to be sidelined this weekend.
Southampton are likely to be without Cedric, Shane Long and Jay Rodriguez at Anfield, as all three have minor injuries.
“It’s not looking good [Cédric’s eye], because it’s still all the colours you can get on your eye, but he can train normally and that’s no problem,” Koeman added.
“We still have the same injuries what we had last week, with Shane Long. Jay is a little bit struggling with his foot at the moment and we have to wait for the weekend.”
Southampton go into their match with Liverpool having lost just once in their last seven matches, and a victory on Merseyside could push them up as high as fifth.