The 26-year-old was hoping to make a return on Thursday from a knee injury which has kept him sidelined since 4 October.
However, the England international has been sent for a scan after complaining of discomfort in a foot.
“I don’t know too much about the situation,” said Liverpool manager Jurgen Klopp.
Speaking after Liverpool’s 2-1 win over Bordeaux secured the Reds a place in the last 32, Klopp added: “It wasn’t a situation I saw because we trained in two groups – the starting line-up and the other players.
“It was really close to the game when the news came. At the moment we have to wait.”
Sturridge has made three appearances this season and only 18 in 2015.
His only goals this season came when he scored twice in a 3-2 Premier League home win over Aston Villa on 26 September.
Before Liverpool’s Europa League game against Bordeaux on Thursday, manager Jurgen Klopp told BT Sport: “We trained this morning, we were at the hotel and he had to leave to have a scan. We have to wait for the results.”
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