According to TEAMtalk, Jose Mourinho wants to bring Dalot to Real once he is officially announced as manager, while Bayern Munich and Barcelona are also exploring a deal for the Portuguese international.
Michael Carrick has already shut down any transfer speculation, though, with the same report revealing that the United boss has "strongly communicated" to the club that Dalot is part of his long-term plans at Old Trafford.
The 27-year-old has seen an increase in performance levels since Carrick became interim boss in January, and now that he's about to embark on the role full-time, the right-back looks set to stay.
Of course, Real's interest in the player could throw a spanner in the works as they look to replace long-serving Dani Carvajal, but it could take a decent offer to prise him away.
Dalot is under contract at United until June 2028, so it may be wise to give him a new deal if he does want to remain at the club.