The Argentine has been out of work since he was sacked by Spurs in November last year and is waiting for the right opportunity to return.
The 48-year-old was linked with Newcastle United before their proposed takeover fell through and was even touted as Quique Setien's potential successor at Barcelona before Ronald Koeman was appointed.
But when asked about Real Madrid, Pochettino told Cadena COPE: "I don’t know [if I will coach Real Madrid one day].
"Football takes you where it wants to take you. If you asked me whether it was a dream for me, of course it is. Like coaching the Argentine national team.
"Real Madrid, if not the best, is one of the best teams in the world. One of the best clubs, with a fantastic history.
Pochettino has been heavily linked with Madrid in the past and is considered more likely to coach Real than Barcelona due to his ties with Espanyol.
"There’s no doubt that any professional who coaches teams, [Real Madrid would be] on their list of dreams when they go to sleep, they would shoot that thought to the universe, to see if it comes true." he said.
"I’m no different to anyone else [in that respect]."