The 21-year-old was left out of France's 4-1 Nations League victory over Belgium on Monday after feeling a strain in his left hamstring during training. The French Football Federation described the issue as a "strain to his left hamstring", while head coach Zinedine Zidane said Jacquet was "slightly injured".
Jacquet had made a strong impression during his first senior international appearances, featuring in France's previous two matches against Italy and Belgium before being ruled out of the second meeting with Belgium.
Liverpool will now wait to discover whether the defender will be fit for Sunday's meeting with City at Anfield.
Jacquet has started six of Liverpool's seven matches this season, partnering Virgil van Dijk in central defence, making his potential absence another concern for head coach Andoni Iraola.
The Reds do have options in defence, with Ronald Araujo available following his loan move from Barcelona and Joe Gomez providing further cover.
However, Jacquet's fitness is only the latest issue for the Merseysiders ahead of City's visit. Alexander Isak was sent home early from Sweden duty with a minor thigh problem, while Cody Gakpo suffered an ankle injury with the Netherlands.
If neither forward is available, Iraola could have to use Bradley Barcola through the middle, despite the recent arrival being more accustomed to playing out wide, or push Florian Wirtz higher up the pitch from his usual No 10 role.
Liverpool will hope Jacquet's hamstring issue proves minor as they prepare for a high-profile clash with City.