A thigh problem prevented him from playing any further part in the Reds’ ultimately unsuccessful bid for a first top-flight crown in 29 years.
He did briefly return to action during a continental meeting with Barcelona at Camp Nou, but played just 11 minutes off the bench.
Klopp had been reluctant to take any unnecessary risks with the South American, but felt his hand was forced during a 3-0 defeat in Catalunya.
Liverpool were able to turn that tie on its head without Firmino, as they booked a final berth with a stunning 4-0 victory at Anfield.
They are now counting down the days to a meeting with Spurs at Wanda Metropolitano on June 1.
It may be that Firmino is welcomed back into their plans for the trip to Madrid, with the Reds posting a positive update on the 27-year-old forward.
Liverpool, who are taking in some warm weather training, said in a statement on the club’s official website: “Roberto Firmino today trained alongside his teammates following a muscle strain that ruled him out of Liverpool’s last three matches.
“The Brazilian took part in the Reds’ first session of their Marbella training camp on Tuesday morning as he works his way back to full fitness.
“Firmino has been working with the club’s medical staff on his rehabilitation from the issue and his reintroduction into full team training will be carefully managed under their supervision, with specialised programmes planned over the coming days.”
Firmino had already offered an update of his own which suggested that he was pushing for a place in Klopp’s thoughts.
He took to social media to post a series of video clips that showed him stepping up his rehabilitation regime.
With the Brazilian running again and working with a ball, he has been welcomed back into the fold by Liverpool.
His return represents a welcome boost for the Reds, with it possible that they could reunite Firmino with fellow forwards Sadio Mane and Mohamed Salah against Spurs.