Chiesa only moved to Liverpool in August from Juventus, but has suffered 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 says Inter are keen to set up a loan arrangement for Chiesa over the January market.
Inter would seek a straight loan for the Italy international to the end of this season.
Reds manager Arne Slot has said of Chiesa: "He missed a complete pre-season, I said this many times, and going to a league where the intensity might even be higher than the Italian league. We just faced the two Italian teams so I can say this now.
"So that makes it difficult for him to make the step towards the intensity levels the rest of the team is at at the moment.
"That has not so much to do with the Italian league or the Premier League, that has more to do with him missing a complete pre-season and that is so difficult for every player – when the games are constantly there – to build them up towards the levels we are at."