The winger was released by Senegal this week after complaining of an injury while away on international duty.
Mane suffered an injury in October, again while away with his country, and the club's medical staff are now awaiting his arrival on Merseyside before they can assess him.
He helped his country reach the World Cup in Russia last week but the former Southampton may now miss the chance to play against his former side on Saturday at Anfield.
Klopp admits the Reds are not willing to take a risk on Mane if he is not 100 per cent fit and you can back the Saints to win using your free bet.
"First and foremost, I have to say big congratulations to Senegal on the achievement of qualifying for the World Cup; this is fantastic news for their country and the players - Sadio included," Klopp told Liverpool's official website.
"Specifically on him returning to Melwood early to be with us; obviously it is a concern that the hamstring injury is again on the agenda and it will be critical for us to monitor and manage that in the coming days.
"At this stage we haven't seen Sadio yet to properly assess the extent, but what is clear is that we will have to stay on top of this for the rest of the week and make sure we are careful in how we look after him.
"So, in this moment all I can really say with certainty is that we will assess Sadio as soon as he lands back in the country and make decisions on what rehab and treatment gives him the best chance of being back fit and strong for the important fixtures we have coming."