United boss Ole Gunnar Solskjaer had been linked with a move for the left-back, who spent last season on loan at Sevilla.
Luke Shaw and Brandon Williams impressed at times last season though Shaw has previously come under heavy criticism during his time at Old Trafford.
Real Madrid are reportedly willing to listen to offers in the region of £27m for Reguilon with Zinedine Zidan having Marcelo and Ferland Mendy ahead of him in the pecking order.
United are believed have a stronger chance of signing Reguilon, 23, than Sevilla due to the Red Devils’ financial power.
And respected transfer expert Fabrizio Romano has tweeted that “Reguilon has been offered to Man Utd”.
There had been suggestions that Real still rate the left-back highly and would want to include a buyback option or a sell-on clause.
But United could improve their chances by selling Chris Smalling, raising funds for a potential move.
Smalling spent last season on loan at Roma and impressed for the Serie A giants throughout the campaign.
Roma made it clear early on that they wanted to sign the Englishman on a permanent deal, but refused to meet United’s asking price of £20m.
Though reports in Roman suggest that the two teams will come to an agreement, although they are still apart in their valuation.
United boss Solskjaer said of Smalling: “I think Chris has shown over his career how valuable he is for Man United.
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"This season was about him being a regular, going to Roma, showing and proving how good a centre-back he is. I wanted to give Harry (Maguire), Vic [Victor Lindelof], maybe Axel (Tuanzebe) a chance, so we found out that was the best for him to go to Roma, play for a year.
“Now he’s coming back and Chris has shown this season that he will be valuable. I’ve been speaking to Chris throughout and been delighted with his season.”