Zinedine Zidane has come under scrutiny after falling eight points behind Barcelona in the La Liga table.
A shock 2-1 defeat to Girona at the weekend increased the pressure on the former France international.
Pochettino, along with Manchester United’s Jose Mourinho, has been linked with taking over at the Bernabeu, if Zidane was to get the chop.
And the Argentine did not rule out a move but instead passed the credit on to his players for getting him mentioned for the post.
"It makes me feel proud of my players because they are the ones who run, the ones who score,” Pochettino said.
Mauricio Pochettino could replace Zidane at Madrid
Real Madrid team predicted to face Tottenham
Tue, October 31, 2017
Express Sport predicts who will start for Real Madrid when they take on Tottenham at Wembley on Wednesday (7.45pm)
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Who will start for Real Madrid when they take on Tottenham at Wembley?
We will need to win so that people recognise that Tottenham aren't only a team that knows how to play well.
Pochettino speaking ahead of Spurs' match with Real Madrid
“The most beautiful thing that is happening to us is that the coaching staff, players and the club see that we all grow at the same speed.
"We came from Southampton, players like (Harry) Kane, Dele Alli, (Eric) Dier, they are getting more mature, the new stadium.
“The potential of Tottenham can not be measured yet. It's a matter of time and of winning.
“We will need to win so that people recognise that Tottenham aren't only a team that knows how to play well."
Spurs face Madrid in the Champions League at Wembley tomorrow evening (7.45pm).
Zidane has come under pressure after recent results
And Pochettino believes it will be a good stage for his side to show the world how far they have come since he took over.
"It will be a very exciting match, as was the Bernabeu,” Pochettino added.
“Not only are three points at stake, but also a good image.
“It is a good opportunity to confirm everything that is said about us and to move on to the next round, which is the goal for Tottenham this season."