The Germany international, who has not played for the Reds since being forced off against Watford in mid-March, will rejoin his team-mates after a spell receiving treatment on a back injury in his homeland.
The 24-year-old missed out on selection for Germany's World Cup squad this week and was thought to be done for the season, although Reds boss Jurgen Klopp has not yet ruled him out of his plans for Kiev.
Can will be assessed by the club's medical staff before a decision is taken about whether he's able to return to full training in Spain.
And, even if he is, the ex-Bayer Leverkusen star is battling against the clock to prove his fitness in time for the clash with Real Madrid at the Olimpiyskiy on May 26.
Can is widely expected to leave Liverpool on a free transfer later this summer, having rejected fresh terms from the Reds, so may already have played his final game for the club.