Speaking on Sky Sport Italia last after Pirlo scored in the 3-2 win over former club Milan, Vialli suggested a move to the Premiership was a possibility.
“I’ve heard rumours from England that there has been contact between Pirlo and Tottenham for next season,” said the ex-Old Lady captain.
The 34-year-old’s future in Turin is unclear at this moment in time given that his contract is set to expire.
The playmaker signed a three-year contract with the Bianconeri in 2011 when he left the San Siro giants on a Bosman free transfer.
Juventus and Pirlo are understood to have put talks regarding a new deal on hold until the start of next year.
The Italian international is ready to put pen to paper on new terms at the Juventus Stadium, but he wants games in return.
“I’ll certainly play on, we’ll just have to see where,” he told the Gazzetta dello Sport in August.
“Juve are my priority, but I don’t want to be a weight for anybody. The years go by, but it is not written that I have to stay here just because I am called Pirlo.
“I want to feel important and a part of the side’s success, otherwise I’ll leave. But I want to underline that it won’t be a problem about money or choosing between one club and another.
“If I had to change, perhaps I’ll go abroad. I’ll certainly continue playing for a high level team.”