The 21-year-old winger, who is the son of former Italy international Enrico Chiesa, has been registering on the transfer radar of leading sides across Europe for some time.
Juventus are eager to ensure that Chiesa does not leave his homeland, with the Turin giants readying a bid to keep him in Serie A.
There is an intense rivalry between the Bianconeri and Fiorentina on the field, but the professional relationship between the two clubs off it is considered to be positive.
Juve were able to land Federico Bernardeschi from La Viola in the summer of 2017 and are weighing up another move down a move for another of their stars.
It is expected that an even bigger fee than the €40 million (£34m/$45m) Fiorentina shelled out two years ago will be required in order to get a second deal done.
Current valuations put Chiesa’s price tag at between €60-€70 million (£51m-£60m), although the Della Valle family at the helm in Florence could push that figure up.
With that in mind, no formal approach has been made as yet.
Instead, Juventus are prepared to let another transfer saga play out naturally.
The Bianconeri will wait and see how the market shifts before deciding on their plan of attack.
Outgoings will, after all, have to be taken into consideration before any incomings are put in place.
Speculation continues to surround the respective futures of Douglas Costa and Paulo Dybala in Turin, with it possible that they could take on new challenges when the window re-opens.
If that proves to be the case, then Juve are ready to ready to make another addition in Chiesa, who has netted 12 times in 31 outings this season and has passed the 100 appearance mark in Serie A.
Not only is the striker an extremely impressive player at the moment, but at 21 he is only expected to improve in the future.
He is currently tied with a contract until 2022 with Fiorentina and it will not be easy to break that agreement.
Juventus are, however, willing to step up their interest after making it clear that Chiesa is now a top target.