Firmino has been out of action for a month because of a knee injury, playing most recently in the home defeat against Chelsea on 4 March (AEDT).
The champion sits seventh going into the away clash with Arsenal, five points adrift of the top four, though it hopes a win at Wolverhampton Wanderers prior to the international break will prove a turning point after a miserable run of results.
"Bobby [Firmino] is back," Klopp said on Saturday (AEDT), and he was also asked about other injured players such as Jordan Henderson and Virgil van Dijk.
"All the others not and I have no idea about the Euros. Nothing has changed.
"They are all in the place they should be at the moment. I don’t have bad news or brilliant news. If they are ready then they are ready. They are in rehab process.
"Jordan is not here at the moment, he cannot train. He will train in the next days or weeks, for sure."
In the absence of Firmino, Diogo Jota recovered from his own injury to score against Wolves and help the Reds to secure UEFA Champions League progression against RB Leipzig.
He followed up that form with three goals in two caps for Portugal.
"Diogo is in a good moment," Klopp said. "It's good. These are the real benefits of an international break.
"Shaq [Xherdan Shaqiri] played well for Switzerland. Thiago played a good role in the Spanish games.
"So there are benefits, but not a lot. Scotland played well, Wales surprise three points - a lot of things were going on.
"I will speak to [Curtis Jones after his red card for England Under-21s].
"You don't want to see these things after a game but we all know in a moment when you lose a game, and it meant a lot to Curtis, who played really good game - if the other team didn't do anything there would be no reaction.
"We have a tough programme, it is always a challenge coming back from international break. You have one session to bring it all together. There is no guarantee that it always works.
"We were here, they are back, train again and go again."
Arsenal won this fixture 2-1 last season and is looking to beat Liverpool in consecutive home league games for the first time since April 2015.
The Reds have won just two of their past 20 Premier League away games against Arsenal (D9 L9), while the Gunners have lost only one of their past eight home Premier League encounters.
Arsenal, though, has gone eight top-flight matches without a clean sheet and has conceded the first goal in four of its past five league games.
Unusually, Liverpool has fared better on its travels than at Anfield for much of this season, with its past five league victories all coming on the road.
Klopp added: "Let’s go for it and have a look at the end. We don’t have a lot of points to waste any more. We will not hesitate and we will just go for it.
"We are not living in dreamland, but if you ask me what do I wish for, let's go with all we have.
"Whoever plays away at Arsenal should never expect the points, but whatever we want, we only get if we win football games.
"Arsenal is a quality side, they have a lot of potential, quality, experience, youth, really exciting team.
"The Premier League is a tough league. If you are not at the top level, you get punished.
"It’s a tough one, but should be tough for Arsenal as well. Our only intention is to be exactly the opponent Arsenal doesn't want."