Chiesa was only sold by Juventus to Liverpool in August, but he has struggled with form and fitness in England.
Calciomercato.com says that a return to Serie A has now been promised for Chiesa.
Napoli chief Giovanni Manna is a fan of Chiesa and wants to bring him back to Italy during next month's winter market.
Manna has held discussions with Fali Ramadani, Chiesa's agent, about the prospect of a loan deal.
Napoli are unwilling to pay the player's full salary, so Liverpool will have to pay part of it if a loan has to be negotiated.
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