The forward resumed full team training this week following a short layoff due to a foot injury sustained during the Emirates FA Cup semi-final with Manchester City on April 16.
Asked if Firmino could come into contention for the visit of Spurs, Klopp told reporters: "I don’t know, but he is back in training, so now we have to make a decision about that.
“The foot thing didn’t let him do a lot. We had to let it settle and now we have to make sure that he has a few proper sessions. Obviously we have enough games still, so it's very important that we have to make sure that we get him in the best possible shape.
“I didn't make a decision but it might be possible, that it makes for him more sense just to train through the weekend and be then a big step closer for Tuesday, for example.
“But let's see. Yesterday he was in training, was great.”
Elsewhere, Liverpool have no fresh injury concerns to contend with following Tuesday’s Champions League semi-final, second-leg win over Villarreal in Spain.
Mohamed Salah could make his 250th appearance for the Reds in all competitions, while a clean sheet for Alisson Becker would equal his Premier League record of 21 in a single season, set in 2018-19.
Tottenham will be without Sergio Reguilon for the trip to Anfield due to a calf complaint.
“He is not available,” said Antonio Conte at his pre-match press conference. “He hasn’t had a training session with us. He is not available. I honestly don’t know – there are only two weeks before the end of the season – whether it is possible for him to come back.”
Conte confirmed Spurs do not have any other fresh injury concerns ahead of the game, though Matt Doherty, Oliver Skipp and Japhet Tanganga have already been ruled out for the remainder of 2021-22.
“We prepared the game very well and I think we need to be very good without the ball to be good defensively, but if we want to win we have to be very good with the ball,” he added.
“I said this to my players, we need to play a good game and be brave when we have the ball, don’t be scared for all the pressure and to find the solution.
“We have improved a lot. We can go there to play and try to get three points. We are in this race for a place in the Champions League and for this reason we need to get points in every game. Every game is a big chance for us to improve the table. In this game we have to try to beat Liverpool.”
Last match
Villarreal 2-3 Liverpool (May 3): Alisson, Alexander-Arnold, Konate, Van Dijk, Robertson, Fabinho, Thiago, Keita, Mane, Salah, Jota.
Tottenham 3-1 Leicester City (May 1): Lloris, Davies, Romero, Dier, Emerson, Bentancur, Hojbjerg, Sessegnon, Son, Kane, Moura.