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.
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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.