Can returned to training last week following a two-month spell on the sidelines, while Milner missed the Reds' final league game of the season due to a minor problem.
Both midfielders are back in contention to face Madrid in Kiev on Saturday night, however, providing Klopp with a major boost in an area that he was already light due long-term layoffs for Alex Oxlade-Chamberlain and Adam Lallana.
"Millie was clear [he would be fit] and Emre is a surprise," Klopp told the club's official website. "He told me he would come back, try this and that and then we would talk to people.
"We thought it would be difficult, but he came back and from the first day it was like, 'OK, that looks good, how do you feel?' 'Very good' and then the next day 'very good' again.
"Now he trains completely normal. He's a nice option and that's why he is with us."
Lallana may yet play a part for Liverpool at the NSC Olimpiyskiy Stadium, having been given a 16-minute runout against Brighton & Hove Albion a fortnight ago.