The Red Devils have emerged as a leading candidate for the impressive Reguilon, who shone on loan at Sevilla last season.
However, Reguilon has been hesitating on a move to Old Trafford because he still dreams of playing for Madrid.
A loan return to Sevilla was mooted, but the Andalusian club are signing Marcos Acuna from Sporting.
Marca journalist Jose Felix Diaz says talks have intensified between Madrid and United for the 23-year-old.
A transfer fee is still under negotiation, but will be in the region of €25m (£23m).
Madrid’s still want to include the option to buy Reguilon back after one or two seasons.
United are not the only Premier League side to have shown interest, but have been the more persistent with Reguilon’s new agent Kia Joorabchian.
Reguilon is currently at home in Valdebebas recovering from a minor injury suffered on international duty.