Goodison Park officials have contacted the Serie A champions about the availability of the Italy international, according to Goal.
Juve’s asking price of €40 million including bonuses has not put off the Toffees, who are expected to resume talks shortly.
The Turin club are looking at raising some funds after splashing out more than €100 million on the signings of Matthijs de Ligt, Mehri Demiral and Luca Pellegrini.
Kean’s sale would bring in a significant sum, while Gonzalo Higuain and Mario Mandzukic could also be sacrificed before the end of the transfer window.
The stumbling block for Everton so far has been Juve’s insistence on inserting a buyback clause into the deal, something the Premier League side will not consider.
However, the Merseyside club remain optimistic that an agreement will be reached which will satisfy both parties during talks on Monday.
Kean broke into the Juve team last season, scoring six goals in 13 Serie A appearances to earn his maiden Italy call-up before hitting two goals in three Azzurri outings.
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