Chiesa only moved to Liverpool from Juventus in August but has had an injury-plagued start to his Premier League career.
The Italy international has played just 78 minutes of football for the Reds but is a target for the Nerazzurri.
Tuttosport say Inter are keen to finalize a loan deal for Chiesa for the January market.
Inter are said to be seeking an immediate loan deal for the Italy international until the end of the season.
Reds manager Arne Slot has said of Chiesa: “He missed a complete pre-season, I've said that many times, and went to a league where the intensity could even be higher than that of the Italian league. We just faced the two Italian teams, so I can say this now.
“So that makes it difficult for him to step up to the intensity level that the rest of the team is currently at.
“That's not so much to do with the Italian league or the Premier League, it's more to do with the fact that he's missing a complete pre-season and that it's so difficult for any player – when the games are constant – to play them. to build to the level we are at.”
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