Real said they were "surprised by the demonstrations" made by Pochettino about a "supposed request" to stay at their training ground.
The Argentinian also joked that Perez had offered to let him stay if he ever chose to coach the Spanish giants.
It seems as though Pochettino's comments were made in jest but interpreted as serious by Real Madrid.
"Real Madrid wants to make it clear that it is completely false that this request has been made".
"At no time has our club been requested that these teams could be accommodated in the facilities of Ciudad Real Madrid", they added.
"Real Madrid also wants to emphasise that the accommodation for the finalists of the Champions League is assigned by UEFA following organisation and security criteria".
Spurs will train at the Spanish giants facilities as they prepare for the final in Madrid, however, Pochettino insists he is focused exclusively on Tottenham despite a half-hearted comment from Real president Florentino Perez.
In a light-hearted part of the interview, Pochettino was asked if Tottenham's players would also stay at Valdedebas.
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"Ahead of the final, we will train at Valdebebas and sleep in a nearby hotel", Pochettino said.
"I asked Florentino [Perez, Madrid president] to let us sleep in the sports centre, but he told me that I can only sleep there when I become the coach of Real Madrid".
Off the pitch, Tottenham have had a rather turbulent build-up to the European final.
Pochettino was heavily linked with the vacant position of Real Madrid coach last season when Julen Lopetegui and then Santiago Solari were sacked.
Jose Mourinho believes Tottenham could go on a trophy spree if they can win the Champions League final next week.
Winks' availability will hand a major boost to Mauricio Pochettino as he looks for a way to get past Liverpool, who beat Spurs home and away in the Premier League this season.
"Logically, we wanted to be competitive. We used to say finals are not to play, finals are to win". "However, no bet would've chosen Tottenham in the final".