The recently-capped Spain international is back at Madrid after starring on a season's loan for Europa League winners Sevilla last season.
Reguilon is not part of Zinedine Zidane's immediate plans, though, while Sevilla pulled out of the running for his permanent signature due to a lack of funds.
That left Man United as the strong favourites to sign the 23-year-old, but The Athletic claims that Spurs have got to the defender first.
While an agreement is not yet in place, a transfer is described as "highly possible" and Jose Mourinho is confident of getting the deal over the line.
Spurs kicked off their 2020-21 Premier League campaign with a 1-0 home loss against Everton on Sunday.