Liverpool confirmed on Thursday that midfielder Lallana - who signed from Southampton in a deal thought to be worth around £23million earlier this month - is expected to be sidelined for up to six weeks after sustaining lateral collateral ligament damage in a training session in the United States.
Should the England international be unavailable for six weeks, he will miss his new club's first three games of the Premier League season against former employers Southampton, champions Manchester City and Tottenham.
A statement published on Liverpool's official website read: "[Adam] Lallana has been assessed by Liverpool's medical staff and does not require surgery.
"No specific timeframe has been placed on a return to fitness, but injuries of this nature can result in a spell of anywhere up to six weeks on the sidelines."
The 26-year-old did not feature in Liverpool's opening game of their pre-season tour of America - a 1-0 defeat to Roma in Boston - but manager Brendan Rodgers had hinted he was in line to play against Olympiacos on Sunday.
However, Lallana will now undergo further assessment in the US before returning to Merseyside.