Firmino has been sidelined since the 2-0 win over Inter Milan in the Champions League, which saw him come off the bench to score the opener at the San Siro.
But having come through that 45-minute appearance, the striker has since missed the last four games, and is set to sit out the visit of West Ham this weekend, too.
Liverpool have coped well in his absence, scoring 11 goals and lifting the League Cup, but his return to the fold will be much-welcomed.
And despite Firmino being ruled out of the clash with West Ham, Klopp has revealed that he could be back involved for the second leg against Inter on Tuesday night.
“Bobby is looking good, but not good enough for the weekend,” he told reporters on Friday.
“I think the plan is that he trains on Sunday first time [for the] full [session]. That sounds, then, doable for Tuesday.”
It is likely that Firmino will take a place on the bench for the Champions League last-16 decider, with his comeback boosting Klopp’s attacking options further.
The manager is already able to call upon Mohamed Salah, Sadio Mane, Diogo Jota and Luis Diaz, along with the backup duo of Divock Origi and the in-form Takumi Minamino, which has allowed him to rotate his starting options throughout a busy run.
Mane has deputised as No. 9 in recent weeks and impressed, which could give Firmino a new challenge to consider when he is back fit, having already seen Jota battle for a spot up front.