The Mirror reported on Monday [15 January] that Spurs were "confident" of agreeing a deal to sign the 18-year-old, who has made just six senior appearances for the League Two club, the latest coming in the FA Cup third round replay loss to Reading.
But The Independent claim that suggestions Tottenham are closing in on a deal are untrue, with Wilmot's long-term future still up in the air. Liverpool, who had previously been mentioned with an interest, remain keen on signing the centre-back while Southampton are also tracking the academy product.
Stevenage are consigned to Wilmot leaving Broadhall Way, with forwards Mark McKee, Ben Kennedy and Matt Godden all expected to follow.
Chairman Steve Wallace is however unwilling to allow any of the quartet depart on the cheap and wants a fee similar to the seven-figure sums which saw Matt Grimes and Ollie Watkins leave Exeter City for Swansea City and Brentford respectively.
"Spurs, Arsenal, Chelsea, Liverpool, Burnley, Watford, Brighton, Bournemouth and West Brom have all registered interest and I am told there is also a top Bundesliga club that wants to speak to me," Wallace said in a statement last week.
"To me, Exeter City set the bar for us all in League Two with the sale of 19-year-old Matt Grimes at £1.75m and they did it again with Ollie Watkins last season at £1.8m.
"This is the value of a young lad today with Premier League potential, no matter what league his club are in, with an individual package for the player that reflects the size of the fee. The days of top quality young lads being picked off early for relatively small fees and modest wages are over, reflecting the inflated value of a Premier League player today.''
Despite Stevenage's valuation of Wilmot, reports have claimed a fee of £850,000 could be enough for Liverpool or Tottenham to tempt him away from the fourth-tier side who he joined in 2014 as a scholar.
After being named as an unused substitute for a handful of games last term, Wilmot was finally given his senor debut in the EFL Trophy penalty shoot-out defeat to Milton Keynes Dons, before a run-out against Tottenham and Liverpool's Premier League rivals Brighton and Hove Albion in the same competition.
He made his league debut in the 1-1 draw with Morecambe last Saturday [13 January] but it is in the FA Cup where Wilmot has made his name, following up a cameo appearance against Nantwich Town with a man-of-the-match display in the goalless draw with Reading in the third round.
Though he was part of the side which was dumped out of the competition at the Madejski Stadium on Tuesday [16 January] after a 3-0 loss to the Championship outfit, Wilmot completed just the third full 90 minutes of his career in the tie to further enhance his claim for a move to a higher level.