The Argntinean was a front-runner for the Bernabéu job before Real settled on Julen Lopetegui and stayed at Spurs to remain true to his values.
Mauricio Pochettino said he did not join Real Madrid last year because he refused to break his contract with Tottenham.
Pochettino was reportedly a leading contender to take charge of Madrid following Zinedine Zidane's shock departure after leading them to a third consecutive Champions League title.
But Los Blancos instead plucked Julen Lopetegui away from Spain days before the World Cup, with the Argentinian remaining at the helm of the Premier League side.
Pochettino confirmed Madrid were interested in giving him the job but said Spurs chairman Daniel Levy rejected their approach.
"The situation was difficult. The dream of every coach was at stake: to lead the biggest team that exists," Pochettino said in an interview with El País.
"And you must say no. That is momentous. It creates a conflict. Because you know that if a coach wants to leave, he leaves. But I had just signed a [contract] renewal with Tottenham. And I felt that I could not do anything.
"Daniel Levy did not accept the offers to free me and if they ask me to break the contract I cannot accept it because I cannot behave like that.
"If my chairman thinks I'm going to continue, I'm not going to run off. Those are not my values. Why is it going to be good for a club to sign a coach who violates his commitments?"
Pochettino persuaded Spurs stars to stay
Spurs have not made a single signing in either of the last two transfer windows but Pochettino has still led the club to their first Champions League semi-final this season.
He revealed some of the club's players had signalled their intention to move on last year, only to be persuaded to stay at Spurs.
Pochettino said: "They called me during the World Cup and they said to me: 'I'm leaving.' I said: 'Talk to the chairman.' They said: 'Yeah, but I want to tell you because I'm excited to go and play for this or that club.'
"I told the chairman: 'Be wary of the player who wants to stay, not the one who wants to leave, because the one who wants to go to a big club often does it because he is ambitious and wants to win titles, and that is the kind of player Tottenham needs because that player is also the one who is going to deliver to the maximum.'
"Then pre-season begins, the transfer window closes, the exits do not materialise and there are no signings. So we all sit down and there you have very few options. Either we all start from scratch or we keep going with what has been happening for two years."
Pochettino has indicated he would consider leaving Spurs if they won the Champions League, with his side taking on Ajax in Amsterdam on Wednesday after losing the first leg 1-0.