Liverpool have been without Coutinho since the Brazilian picked up a hamstring injury during their 4-1 win over Manchester City late last month.
"Philippe had a very intensive session (on Saturday) but we decided two or three days ago that we didn't want to risk (him) for this game," Klopp told reporters after the Swansea game.
"Now I think he's fit. I saw him in the dressing room and he looks good. I'll have to talk with him tomorrow – I think he's ready for Southampton," the German added.
The win, which came thanks to James Milner's second half penalty, moved Liverpool up to sixth on 23 points, two adrift of fifth-placed Tottenham Hotspur.
Klopp said the windy conditions had not helped his side at Anfield and added that the result was the most important thing.
"I was only on the pitch during the warm-up but it was really crazy because it changed all the time, he said.
"We are an outdoor sport, no problem, we have to accept all rain, snow, wind, whatever. But it's the biggest enemy of football, wind."
(Reporting by Simon Jennings in Bengaluru; Editing by Peter Rutherford)