Everton and Crystal Palace have previously been credited with interest in the goalkeeper, but Spurs are also looking to strengthen in that department having opted not to re-sign Pau Lopez.
Woodman warms up for Newcastle
Woodman is currently third-choice at Newcastle, who it is claimed are chasing a new number 1 ahead of the transfer deadline.
And that could leave the England Under-20 talent - who is said to have requested a loan move this season - even further down the St James' Park pecking order.
Having also sold Luke McGee to Peterborough United this summer, Tottenham have begun the campaign with only Hugo Lloris and Michel Vorm as senior options between the sticks.
And with Spurs set to compete in four competitions this season, Woodman would perhaps stand a greater chance of breaking into Mauricio Pochettino's plans than he would Rafa Benitez's, while the prospect of succeeding Lloris as number 1 in the coming years could also attract the 20-year-old.
Woodman's father, Andy (right), at the pair's previous club, Crystal Palace
Woodman's father, Andy, Newcastle's former goalkeeper coach, was recently hired by Tottenham's local rivals Arsenal, which should only increase the appeal of a return to London, the city in which he grew up.
Newcastle's keeper search is reportedly being held up by their failure to offload Tim Krul, who is now below Woodman as fourth-choice, and selling the youngster could be seen as an alternative way to raise funds.