The Italian side are long-term admirers of the South African who is out of contract next summer and free to talk to foreign clubs from January 1.
Juventus have struggled so far this season and are keen to bolster their squad further in the next window.
Hot property: Everton star Steven Pienaar
That could tempt them into a January bid for Pienaar even though they know they could sign him for free in the summer.
The 28-year-old has been in good form for Everton but is unwilling to sign the contract the Goodison Park club have offered.
Tottenham remain keen and will press hard for the player but, if Everton refuse to sell in January, they could face further competition from Manchester United, Arsenal and Liverpool in the summer.
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