It’s claimed the Premier League club are among those who have been watching the 19-year-old Dane.
Interest in the 6ft 5in star, who has just signed a long-term deal at Town , comes as no surprise.
Billing has been regarded as a bright prospect ever since moving from Esbjerg in 2013.
But Town have him under terms through to 2020 after he put pen to paper on a new contract only last month.
Billing, who has one Denmark Under 19 cap, has flourished under David Wagner .
The head coach has given him eight of his 12 first-team appearances (seven starts).
His debut came from the bench in the 2-0 Championship defeat at home to Leicester City back in April 2014, when Mark Robins was manager.
But he didn’t feature again until September, when Chris Powell introduced him as a half-time substitute in the 2-1 win at Charlton Athletic.
Billing made his first start in Powell’s final match as manager, the 2-2 draw at Reading in November.
He picked up an ankle injury in the next game, the 3-0 home defeat by Leeds United, which left him playing catch-up in Wagner’s early weeks at the helm.
An eventful campaign continued with a spectacular first Town goal in the 2-0 win at Nottingham Forest in February.
Billing was then shown a controversial straight red card soon after coming off the bench in the 1-1 draw at MK Dons.
After Town failed in an appeal , he served a three-match ban and returned to make a sixth career start in the 4-1 win at Leeds United.
Billing played the whole of the 1-0 home defeat by Sheffield Wednesday at the start of this month and came off the bench in the 3-0 defeat at Middlesbrough.
He was an unused substitute in Saturday’s 2-2 home draw with Hull City.
Tottenham scout Ian Broomfield is said to have been keeping close tabs on Billing.
Spurs have become known for developing young players with England midfielder Dele Alli, signed from MK Dons for £5m 14 months ago, emerging this season.
Transfer business between Town and Tottenham has been scarce down the years.
Town took winger Andy Turner on loan from Spurs in 1995 and signed defender Simon Webster from them 10 years earlier.
Spurs have signed two players from Town, forward Bert Smith in 1919 and winger Jimmy Smailes in 1931.