The Italy international left Juventus for Liverpool on deadline day last year, but struggled for form and fitness over his first 12 months in England.
Chiesa has been left on Merseyside with Liverpool now in Hong Kong for the first-leg of their Asian preseason tour. A slight injury has been identified for the reason for him being left behind.
Sportitalia says Atalanta are ready to act and bring Chiesa back to Serie A for the new season.
The key to any deal will be Chiesa's €5m salary, which is beyond Atalanta's wage budget. The player would either have to accept a pay-cut or insist on Liverpool covering a percentage of his wages.