It was feared the England international had suffered a "serious" injury soon after coming on as a substitute in the 2-1 win at Crystal Palace on Saturday.
"That's not as bad as we thought - a number of weeks," Klopp said.
"It is not the Adam Lallana season so far," Klopp said on Tuesday.
"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."