Mane had only just recovered from the problem that he suffered during the October international break, and has now been sent back to Melwood due to concerns over the same issue.
The 25-year-old helped Senegal reach the 2018 World Cup with a 2-0 win over South Africa on Friday, but Klopp has conceded that Liverpool are 'concerned' by the attacker's latest problem.
"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," Klopp told Liverpool's official website.
"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.
"There has been really strong communication between ourselves and the Senegal team management to ensure the player is properly protected and looked after. We respect how important he is for Senegal and therefore it must always be the case that they get to make the decision when he is under their care.
"It should not be forgotten in Liverpool, either, how important it is to Sadio that he represents his country whenever he is fit enough to do so. He is so proud of his country and recognises what a role model he is for them.
"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."
Liverpool will return to Premier League action with a home game against Southampton on Saturday afternoon.