The 28-year-old limped out of the Three Lions’ 2-2 draw with Spain on Tuesday, having injured his groin early on in proceedings.
Prior to the St Mary’s showdown, Klopp said the in-form midfielder is likely to miss more than just the Saints match, with Sunderland the Reds’ next opponents at Anfield next Saturday.
“It was serious enough to be not involved today and possibly the next two or three games.
“We don’t know exactly in the moment but that was the only problem we had.”
Lallana has been in scintillating form so far this season, with his influential performances helping Liverpool top the Premier League table currently.
While Saturday’s draw with Southampton was far from solely down to his absence, the Reds didn’t quite have the same flow to their play.
Part of that was down to a lack of cohesion following the international break, but it is clear that Lallana is now one of the first names on Klopp’s team-sheet.