Chiesa moved to Liverpool in August from Juventus, but has struggled for form and fitness since his arrival.
A return to Serie A has been mooted for the Italy international, with Lazio already expressing interest.
Lalaziosiamonoi.it says Liverpool are prepared to listen to offers for Chiesa and would seek to recoup the €15m they paid for the attacker at the beginning of the season.
Lazio would seek to setup a loan arrangement with an option to buy - with Liverpool's asking price within their budget.
However, Lazio would need assistance from Liverpool to cover part of Chiesa's €7m salary to make the deal work.