The 20-year-old French defender, who agreed a £60million move to Anfield last week, will join at the end of the season.
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He went down awkwardly in the second half of Rennes’ 3-1 Ligue 1 defeat to Lens on Saturday, when defender Abdelhamid Ait Bouddal also suffered a muscle injury.
Rennes coach Habib Beye said: “It’s definitely quite serious for both of us.”
Liverpool signed Jacquet in the January transfer window after a deal to sign Crystal Palace’s English defender Marc Guehi fell through last summer.
Chelsea were also interested in Jacquet, who has made five international appearances for the French under-21 team and was described by Liverpool manager Arne Slot as a “great talent”.