The Daily Mail says around 30 scouts attended Stevenage's Checkatrade Trophy tie with Brighton earlier this month to watch Wilmot, who turned 18 on 4 November.
The young centre-back made his first-team debut for Stevenage last month in a goalless draw at MK Dons in the EFL Cup. He is yet to play for the club in League Two.
Stevenage manager Darren Sarll praised Wilmot's performance in the 3-1 win over Brighton earlier this month.
"Wilmot has just turned eighteen and he was absolutely terrific," Sarll told the Comet newspaper.
"He plays like a thirty-year-old, he's got a wonderful, mature outlook on the game and I thought he was absolutely terrific.
"As a young lad you should want to show that enthusiasm and that urgency. If we can get that enthusiasm and urgency out of Ben... and the other young players then we'll have some really terrific young players for the future."
Liverpool boss Jurgen Klopp has been urged to address his team's defensive issues in the January transfer window or risk losing out on a top-four spot in the Premier League.
The Reds have been linked with a £60m ($79m) move for Southampton defender Virgil van Dijk, although they are likely to face competition from Manchester City.
Klopp's side squandered a three-goal lead to draw 3-3 against Sevilla in the Champions League in midweek and host Premier League champions Chelsea at Anfield on 25 November.
Former Chelsea winger Pat Nevin ruled out the chances of the Reds winning silverware this season if they do not address their defensive issues.
"Liverpool won't be winning anything, challenging for the title and possibly missing out on the top four if they leave this [centre-half situation] too long," Nevin was quoted as saying by the Sport Review in October.
"They will be out of the top-four race if they're not careful before the end of the year."