Salah was substituted in the second half of the 2-0 victory, minutes after scoring the second goal with a penalty.
The Egyptian's foot was swollen after the match but Klopp said he had been told Salah would be rejoining team training.
"Mo is a tough cookie. We were quite happy and lucky. (It was) swollen, painful, today less so," Klopp told a news conference on Tuesday. "I got a message before the press conference he's ready to train. We'll see how that looks."
Liverpool are second in the table and can cut Manchester City's lead at the top to a point if they beat fourth-placed Arsenal after Pep Guardiola's side were held to a 0-0 draw at Crystal Palace on Monday.
"I watched City for exactly 65 minutes for analysis reasons, believe it or not. I don't have time to watch them in real-time," Klopp said. "Palace did well, but so did City, they just didn't finish situations off.
"For the last 30 minutes, I didn't watch but saw the result and was surprised.
"Does it help the mood? Why should it? We play Arsenal and we cannot count points away at Arsenal now ... We have to play this game."
The German tactician backed his team to push City all the way in the title race. The two sides face each other in a potential title-decider at City's Etihad Stadium on April 10.
"That's the plan, of course, that we keep being as annoying as possible," Klopp said.
"We have 10 games to play and there are a few really tough ones. Each Premier League game is tough, but a few are especially tough, one of them we play tomorrow night.
"Can we win all 10 games? It doesn't sound likely, but as long as it's possible, we will give it a try."