The Argentine has been heavily linked with a move to the Premier League in recent weeks, with Arsenal and Manchester City credited with an interest.
However, it now appears he could remain in Serie A as Juve step up their pursuit of the 21-year-old.
The Bianconeri have already had a £25million offer turned down as Palermo hold out for another £4m.
Juve are in pole position
Maurizio Zamparini
Dybala has also attracted interest from Italian clubs Inter Milan, Roma and Napoli, as well as Ligue 1 giants Paris Saint-Germain.
“Right now, Juve are in pole position,” Zamparini said.
“They want to close the deal in a week. But, of course, I want the best possible deal. Dybala is being auctioned.
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Juventus lead the race for Palermo's Paulo Dybala
“The Bianconeri have offered me €35m, put I want €40m or more. I’m also dealing with Arsenal.
“PSG [Paris Saint-Germain] have requested information from Dybala’s agent, they know the player is on the market.
“They’re interested in Paris, just as they are at Arsenal, Manchester City, Juventus, Inter, Roma and Napoli.”
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