Reguilon, who spent last season on loan at Sevilla, is close to completing a permanent switch to north London.
The Evening Standard reports that the defender, 23, arrived at Hotspur Way on Wednesday where he is expected to complete the first part of his medical before finishing it on Thursday.
Reguilon, who was voted the best left-back in LaLiga last season, has also attracted interest from Manchester United.
talkSPORT understands that the LaLiga giants have inserted a buy-back option into the deal, but that clause will need to be activated within the next two years.
Real will also have first refusal on any offers Spurs receive for Reguilon, with an official announcement expected within the next 48 hours.
Bale is expected to join Reguilon at Spurs in the near future
Meanwhile, the Premier League side remained locked in talks with Madrid over bringing former Lilywhite hero Gareth Bale back to the club on a season-long loan deal.
Bale remains a popular figure with Spurs fans after scored 55 goals in 203 appearances during a six-year spell for the club between 2007 and 2013.
talkSPORT host Jim White revealed on Wednesday’s Sports Breakfast he has been told by a source close to Bale that the Welshman’s return to Tottenham WILL happen this summer.
“It’s my understanding that Gareth Bale very much wants this deal to happen,” he said.
“A few moments ago a close associate of Bale’s told me the player is ‘very keen’ on this going through.
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“I then pushed Bale’s close associate even further and I said to him straight: ‘Look, will Bale to Tottenham happen?’
“And the answer I’ve just received is: ‘Of course it will’.
“Bale is still in Madrid, he’s been carrying a slight knee injury, and he showed up for training this morning.
“The rest of the Real Madrid players were there and training started, but he left after 20 minutes.
“So it looks like we’re almost at a stage that we’ll hear Bale is on his way.