Pochettino has worked wonders during his time with Spurs, but his reputation has moved on to another level after what he has achieved with the club this season, despite not signing one player in the summer.
The result against Barcelona in midweek also impressed Real officials with reports claiming they will make another approach at the end of the season, despite only just appointing Santiago Solari on a deal until 2021.
United are also keen as the pressure mounts on Jose Mourinho, and Spurs ace Danny Rose believes Pochettino would deserve his chance with one of those top clubs.
"What he has done here in the last four or five years has been amazing," Rose said. "It's no secret all the teams have spent a lot more than what we have. The manager did not make any signings in the summer and he is probably not going to make any signings in January.
"It speaks volumes of how good he is. It's no coincidence that every day you read Real Madrid want him or United want him. It's exactly what he deserves."