Henderson sustained damage to his lateral collateral knee ligament during Friday's 1-1 UEFA Europa League quarter-final draw against Borussia Dortmund.
A club statement on Friday said Henderson was facing six to eight weeks on the sidelines, meaning an end to his season and casting his participation in England's UEFA EURO 2016 campaign into major doubt.
But speaking at a news conference ahead of the English Premier League match against Stoke City, Klopp was more upbeat over Henderson's prospects.
"It's serious but it's not that serious that there is no hope for us for maybe the last one or two games," he stated. "It's clear there is still hope for the European Championships.
"For us, Hendo is a very, very important player. He's been getting better and better and better in the last few weeks because he's been getting his rhythm. He is obviously an important player for England too.
"There is not a final judgement or whatever so you can say there is no chance (he will play again this season) – there is a chance.
"It is isolated, nothing else. It is not good news but this is part of something like good news. We will do everything for him and for us so that he is back in the race as soon as possible.
"I can't say anymore, you always have to wait. Each day you have to see what you can do or what you have to wait, but until now it's the best you can get when you get a knee injury."
Klopp has Lucas Leiva and Kevin Stewart back among his midfield options for Stoke's visit to Anfield, where he will ponder shuffling his pack with the return against Dortmund coming on Friday (AEDT).
"We have to make a decision about line-ups and systems," he added.
"We have no time for rest so we have to think about a few changes. We'll make decisions after our evening training."
