The report claims Wilmot will head to Vicarage Road in a deal worth £1.5 million, with Arsenal and Tottenham 'thought to have had' offers of around £1 million turned down.
Wilmot made his Stevenage debut earlier this season and has only played 15 times for the League Two side in total.
The 18-year-old has nevertheless caught the eye in that time, and earned his first call up to England's Under-19s last month.
However, Wilmot was withdrawn from the Stevenage squad on the eve of Saturday's fixture against Newport County, with a subsequent club statement reading: "Ben came back from international duty and we have had developments that suggest a deal will be agreed shortly for him to move when the window opens.
"We have had interest from Premier League and Championship clubs, which is not surprising when Ben is recognised by England as being one of the top four centre halves at his age level, with the other three coming from Man City, Chelsea and Spurs.
"We have made public our valuation and the closer we are getting to that the more likely it is that Ben will move."
And Watford would appear to be Wilmot's destination, although he will be unable to feature for the Hornets until the new campaign.
As well as Watford, Arsenal and Tottenham, Liverpool, Chelsea, Burnley, Brighton, Bournemouth have all been credited with interest in the six-foot-two talent.
Will Arsenal and Tottenham rue their alleged Wilmot failure?