Neither player will be fit for Sunday's Premier League trip to Chelsea, but Klopp hopes they will show sufficient signs of recovery next week to be considered for the showdown with Real Madrid in Kiev on May 26.
"As far as I know, nothing else happened [with injuries]," Klopp told a news conference on Friday. "We're all still fit. Adam [Lallana] trained the first real football session at Rome, the morning after the game.
"I've had contact with Emre as well. We can make the decision on Monday if he starts training with us immediately. It could be good news for the final but probably not the last game of the season.
"Joe, we still wait for final assessments. We'll know about that in a few days, probably. But he's not available for Chelsea."
Klopp was keen to praise the form of captain Jordan Henderson and James Milner in recent matches, given Liverpool are without Can and Alex Oxlade-Chamberlain in midfield.
"You cannot be where we are if you have players in these positions who hide," he said. "They showed up because they have the quality to do so, physically, football-wise and in mindset.
"We are really quite thin in midfield and they did a fantastic job, but I'm not surprised."