The 25-year-old joined Liverpool for a fee of around £34m last month, and he has since joined up with the rest of the squad when they reported back for pre-season training last week.
However, the Egypt international will play no part in Wednesday night's Merseyside derby with Tranmere Rovers as he is yet to receive his work permit, although Klopp is hopeful that the situation will be resolved soon.
"Mo Salah is here in training but cannot play because of the rules, so that's what we have to accept," he told the club's official website.
"We will try to get the working permission or the visa, I'm not sure what it is we need to get but we have to go to Paris and leave him there for a day or two and then he'll come back. We are hopeful he can play soon."