Sacked by Juve and replaced by Andrea Pirlo over the summer, Sarri is currently on gardening leave, with his contract running to 2022.
La Nazione says Fiorentina are monitoring developments and will move for Sarri once he is free from his deal.
Currently, his contract is still worth €20m and he is due €2.5m in agreed penalties as part of his dismissal. Juve are keen to clear him off their books and are willing to offer €6m to terminate his deal.
If Sarri agrees, Fiorentina are willing to hand him a bumper signing on bonus to make up for the money lost.
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