The academy graduate has spent his entire career at the North London outfit, making a total of 203 appearances in all competitions.
However, having failed to make a start for Spurs since March 1, the 26-year-old has made been available for transfer by head coach Antonio Conte.
According to the Liverpool Echo, Leeds have become the latest club to show an interest in the England international.
The report claims that Spurs chairman Daniel Levy is attempting to recoup in the region of £20m for a player who still has two years remaining on his contract.
Any interested club are likely to try to lower that valuation, but Leeds will soon have the funds available to meet Spurs' asking price.
Nevertheless, the Yorkshire giants will not have a clear run to winning the race for Winks's signature with Everton also known to be admirers of the player.
At one point, it was claimed that Winks may be included in Spurs' proposal for Richarlison in a bid to reduce their financial outlay on the Brazilian attacker.
However, Spurs confirmed the signing of the 25-year-old on Friday morning for a straight fee, rather than the inclusion of Winks knocking £20m off the £60m deal.
The report says that, as it stands, Everton would prefer to negotiate a loan arrangement with Spurs having only just eased their financial issues with the sale of their most prized asset.
Winks is said to prefer a switch to Goodison Park over Elland Road, a factor which may encourage Everton to stay patient in discussions with their Spurs counterparts.