The Belgium international has been left out of the Spurs squad for the Champions League last 16 first leg trip to Juventus, with The Daily Telegraph suggesting the omission throws his future into major doubt.
Tottenham boss Mauricio Pochettino later confirmed that Alderweireld had been left at home due to having only recently returned from three months out with a hamstring injury. Davinson Sanches and Jan Vertonghen are set to be partnered together at the back in Turin.
But that has not deterred the market, with United installed as the front-runners to acquire the 28-year-old, despite them having the best defence in the Premier League this season.
"Rumours continue to surface that Toby Alderweireld is considering a move away from Tottenham and with Manchester United's defence shipping goals in recent weeks, Jose Mourinho might be seeking reinforcements," said Betway's Alan Alger.
"United are well-backed 4/1 favourites to sign the Belgian centre half ahead of Spurs' London rivals Chelsea, who have been nibbled into 7/1, with PSG at 9/1. Despite Arsenal and Liverpool continually looking shaky at the back, they are less fancied at 16/1 and 20/1 respectively to bring in the Spurs man."
Alderweireld is currently holding talks with Tottenham over a new contract, with his current deal due to expire in 2019, though a clause triggering an additional 12 months will be activated should no extension be forthcoming, according to The Guardian.
A £25m (€28.1m) release clause will also become active, which clubs can prompt if they submit a bid 14 days before the end of the summer transfer window, the report adds. The Evening Standard understands Chelsea are among the clubs monitoring the situation, but Pochettino is confident an extension beyond 2020 will be agreed.
The decision to leave Alderweireld behind follows Tottenham's cautious approach over the recovery of previously injured players, having held back the likes of Danny Rose and Erik Lamela in recent months.
He played the full 90 minutes in the FA Cup fourth-round replay win over Newport County at Wembley in mid-week and insisted he was fit to face Arsenal in the Premier League, but was overlooked completely for the game. Alderweireld's next opportunity could again come in the FA Cup when Pochettino's men travel to League One side Rochdale in the fifth round this weekend (Sunday 18 February).
Meanwhile, United are without Ivory Coast international Eric Bailly due to him having undergone ankle surgery, with Chris Smalling and Phil Jones currently filling the void.
In a summer that saw Romelu Lukaku purchased from Everton and Zlatan Ibrahimovic re-signed on a short-term deal, Jose Mourinho made the relatively low key addition of Victor Lindelof from Benfica, though he has made just seven Premier League starts and has failed to make a sufficient impression.