Lallana suffered the latest injury setback after coming on as substitute in Liverpool's 2-1 Premier League victory over Crystal Palace on Saturday.
"Thank God, that's not as bad as we thought - a number of weeks," Klopp said.
"There is a little hope, of course, that we can maybe use him again this season but we have to wait; it is absolutely not the time to bring any rush into the situation.
"It is not the Adam Lallana season so far. It makes the season so far even more special when you think that we have played the season without him."
Lallana, who sat out the first half of the campaign after suffering a pre-season thigh strain, has started just one league match this season.
England boss Gareth Southgate has to name his final 23-man squad for the tournament in Russia by 4 June.
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