Can trained with the Liverpool squad on Monday and his return to fitness is a boost for Klopp whose midfield options have been restricted by injury to Alex Oxlade-Chamberlain.
But Klopp cautioned about Can's potential involvement in the game in Kiev.
"It depends always on the reaction. But let me put it this way, 10 days ago I didn't think it is possible he could do what he did today. It looked good. It was really positive but we have to wait," he told reporters.
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"The door is open - he is really desperate to be a part. We shall see," Klopp added.
James Milner, who missed the final Premier League game of the season against Brighton & Hove Albion with a muscle problem, also took part in the training session.
(Reporting by Simon Evans, editing by Ed Osmond)
