The midfielder, set to leave the club at the end of the season to join LA Galaxy, was withdrawn midway through the second half of his side's 3-2 Premier League win over Tottenham at Anfield earlier this month.
And, speaking ahead of Liverpool's UEFA Europa League last 32 first leg clash with Besiktas on Thursday, Gerrard ruled himself out of next week's return leg.
"I think I'm a couple of weeks away from returning to playing, but it's settled down well," he told ITV.
"I don't really want to put a target game on the injury.
"I think next week will come too soon."
The issue could leave Gerrard facing a race to be fit for the FA Cup quarter-final against Blackburn Rovers on March 8.
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