The 34-year-old midfielder was tipped as a January target for Spurs boss Andre Villas-Boas after reports emerged claiming Juventus were not prepared to renew his contract.
Real Madrid have also been linked, although the latest report from Corriere dello Sport claims Inter Milan are now interested in bringing Pirlo back to the San Siro.
The Italy international spent three seasons with Inter between 1998 and 2001 before he moved to city rivals AC Milan.
By the time January comes around and the transfer window reopens, Pirlo will have less than six months remaining on his Juventus contract.
As a result, he'll be available for a much smaller fee - similar to when Tottenham picked up Lewis Holtby on the cheap last January from Schalke.
But Spurs will face stiff competition for Pirlo, with Inter able to offer playing time - valuable at this stage of his career - and the opportunity to remain in Italy, where he's spent his entire career.
Tottenham have plenty of options in the centre of midfield as well - Etienne Capoue is currently injured, but Villas-Boas can still call on Paulinho, Sandro and Mousa Dembele.