The Reds are set to take on Bayer Leverkusen in the Champions League group stages on Tuesday.
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Konate had to come off at half-time when they beat Brighton 2-1 at Anfield in the Premier League.
Konate was injured in the game, as teammate Virgil Van Dijk stood on his arm in a corner.
Post-game, Konate wrote on Instagram: "Thanks for all the messages of support.
“My injury isn’t serious thankfully. I had a scan today and it confirmed there is no break. I’ll be ready for the next game."
Konate was replaced by Joe Gomez, who may be hoping to get a start in midweek.