Can is in the final year of his current deal with the Reds, and his representatives have long been in talks with the club over an extension.
But so far no agreement has been made, and with Juventus circling, there remain concerns over Can’s long-term future on Merseyside.
Klopp named his compatriot in his first starting lineup of the season away to Watford on Saturday, and is likely to include Can against Hoffenheim on Tuesday night.
And speaking to reporters on Monday, the German admitted frustrations over Can’s stalled talks, though he insisted he would not be sold.
“So far there is no signing and that is the situation,” he explained.
“We are still in talks. Do I think it is too cool that we didn’t fix it so far? No, to be honest.
“But it is all OK at the moment and we have to take it like this.
“His mind is not elsewhere. It is an important contract for him at his age.
“I am 100 percent sure that we don’t sell the player now in this situation. Not a player from the first team lineup for sure.
“He will play here for the next year that is for sure. All the rest we have to see.”
The suggestion that Can “will play here for the next year” is a worrying one, as Klopp seems to allude to the prospect of the No. 23 leaving on a free transfer.
It has long been Liverpool’s reported stance that they would prefer Can to see out his contract than sell this summer, but Klopp vocalising the situation hammers home its likelihood.
But he stressed that while it is “not perfect,” he is still confident the midfielder will eventually sign a new contract.
“In Germany these kind of pressures come up one year before the contract ends. In England it is two years before,” he added.
“Last year there was no real readiness for negotiations but this year we have talked.
“It’s clear we want him and he also wants to stay. It is about a few little details.
“It’s not about having to make a decision about bringing in another player in the same position, the same size, the same skills.
“Emre is on a good way. He has really improved in a lot of parts and is a really important player for us. He can play different positions.
“The situation is not perfect, I would prefer that he has already signed, but I am still positive we can find the right solution for both sides.”