The Spanish press also report on Wednesday that Real Madrid and Tottenham are also talking about a loan deal to see Gareth Bale go back to White Hart Lane, seven years after leaving the club to join Real Madrid.
They will also have an option to extend the loan for a further season, something which would take Bale through to the end of his Real Madrid contract.
'We now anticipate that he will be match fit after October's worldwide break'.
Reguilón and Bale join a Tottenham side trying to return to the Champions League after failing to qualify for this season's competition because of a sixth-place finish in the Premier League.
He will wear the number nine shirt and form an exciting front-three with England captain Harry Kane and South Korea's Son Heung-min.
Bale flew to London on Friday to finalise the transfer, along with full-back Sergio Reguilon, who Tottenham have signed from Madrid for £27m.
One fan even suggested the manager has "literally tried his absolute best to erase" Bale's achievements at the club.
It has been thought that United headed the chase, but they were reluctant to agree to the buy-back clause, with Spurs having moved quickly following their disappointing 1-0 home defeat to Everton on the opening weekend of the Premier League season.
Welshman Bale left Spurs for Madrid for £85.3m in 2013 but has been frozen out under Zinedine Zidane. I'm not going to now go against what I've always said: that the player has done amazingly.
However, Real Madrid are well-stocked in the position, with Brazil worldwide Marcelo and France's Ferland Mendy already in their squad, so were keen to sell Reguilon to raise funds to balance the books. What an unbelievable club, awesome fans, just incredible to be back. I'm very excited to play.
He added: "I think I am now in the hardest league in the world, the most difficult one".
Gareth Bale will not be able to play for Spurs until after the October global break due to injury.
Reguilon enjoyed an excellent season for Madrid in 2018-19 but Zidane sent the 23-year-old on loan last year to Sevilla, where he helped the club win the Europa League.