The German midfielder came off the substitutes' bench away at Sevilla in the Champions League on Tuesday but is unlikely to feature at Anfield this weekend after complaining of a minor issue.
"We will try until May to keep Can at Liverpool"
Klopp - updating reporters on the fitness of his squad - told reporters in his pre-match press conference that Can "struggles a little bit" with his problem.
"A strange situation in the game, a little muscle [issue]," the manager continued, insisting "it could be close" for Can to feature, Klopp explaining that "he is a doubt."
The 23-year-old has only started one of Liverpool's last four games with suggestions that Can has not featured due to his ongoing contract stand-off.
Juventus and Bayern Munich have both been heavily linked with the Germany international, whose current deal expires in the summer having been in talks to extend his contract for over a year.
Klopp declared that there has still been no progress in their attempts to strike an agreement, but insisted that Liverpool will continue to try to keep Can at Anfield.
"I said he could still sign a contract in May," he told reporters. "That's how it is. Persuade him? That's what we try to do all the time. We have to be as attractive as possible as a club so no-one wants to leave. That's not changed."
Klopp: Matip back in full training
Elsewhere Joël Matip, who has not featured since the win over West Ham United before the international break, and Adam Lallana - still to make his first appearance of the season - could both be involved.
Centre-back Matip has been kept out of the win over Southampton and the European draw in Spain by an adductor issue, with Lallana sidelined since a pre-season clash in August due to a thigh injury.
Klopp insisted there is "no doubt" that Lallana "is on his way" having returned to training a fortnight ago, but warned Liverpool must be cautious over the course of his comeback and "see how we handle this in the next few days and weeks."
He also revealed that Matip trained on Thursday for the "first time with the team" and insisted that he and Lallana "both give good signs" though there is "nothing else to say."
And asked whether the England midfielder might make the match-day squad for the first time since returning to full fitness, Klopp said: "I don't want to talk about this here. If I have anything to say, I will talk to the player first. We will see."