Can has been absent since mid-March with a back problem that has kept him out of 11 games, as well as ensuring he missed out on the Germany squad for the World Cup.
The 24-year-old is expected to leave on a free transfer at the end of the season, and has been tipped to sign a five-year deal with Juventus worth £85,000 a week.
But Can could make his final appearance on the grandest stage, as Liverpool take on Real Madrid in Kiev on Saturday night.
Klopp put his squad through their paces in an open session on Monday, with Can joining the group after having travelled for medical assessments in Marbella last week.
Given he has been out of action for two months it is highly unlikely the midfielder will start at the NSC Olimpiyskiy, but his availability would be a welcome boost for Klopp’s bench.
Youngsters Caoihmin Kelleher, Nathaniel Phillips, Ben Woodburn, Curtis Jones and Rafa Camacho were also in training, with the Reds facing no new injury problems as they prepare for their biggest game since 2007.
Klopp is set to conduct a press conference at 1pm (BST) on Monday, with the manager joined by Mane and Dejan Lovren in previewing the final.
Liverpool Squad Training at Anfield
Goalkeepers: Karius, Mignolet, Ward, Kelleher
Defenders: Van Dijk, Lovren, Klavan, Phillips, Alexander-Arnold, Clyne, Robertson, Moreno
Midfielders: Henderson, Milner, Wijnaldum, Can, Lallana, Woodburn, Jones
Forwards: Firmino, Salah, Mane, Ings, Solanke, Camacho