Zidane is under pressure after a poor run of results that has left his side's hopes of retaining the La Liga title in tatters. Los Blancos are in fourth place in the table, a distant 19 points behind leaders Barcelona, and Pochettino has refused to rule out one day managing the Madrid giants.
He was asked about the possibility of taking over at the Santiago Bernabeu and said, per PA Sport (h/t Sky Sports):
"I am so clear.
"That is my decision because I prefer to work on my farm in Argentina than in some places. But my commitment is massive in this club. I am working like I am going to be here forever.
"But in the end, it is like the players, you never know what is going to happen in football."
Rumours of Zidane's demise have gathered pace after Madrid were knocked out of the Copa del Rey on Wednesday by Leganes, who won the second leg 2-1 at the Bernabeu to qualify on away goals.
The club's only hopes of silverware now lie in the UEFA Champions League where they face Paris Saint-Germain in the last 16.
Zidane may need to win the competition to keep his job, according to La Liga writer Andrew Gaffney:
Dermot Corrigan at ESPN FC said the former France international is in real trouble after the defeat to Leganes:
Zidane must now try to salvage the club's season, but that looks difficult. The club's youngsters and fringe players have not had the desired impact, while the club have missed Alvaro Morata, James Rodriguez and Pepe, who all departed in the summer.
Star men Karim Benzema and Cristiano Ronaldo have also struggled to find their best form, and Gareth Bale has been frequently absent through injury. Zidane, meanwhile, has been slow to respond to his team's struggles and make the changes required to turn their form around.
Pochettino has yet to win a trophy with Spurs but is widely regarded as one of the most talented young managers in Europe due to his success with the club. He has overseen title challenges in the past two seasons and took the team to a second-place finish last year.
The 45-year-old is also likely to have impressed Real Madrid after he guided Spurs to a 1-1 draw at the Bernabeu in the UEFA Champions League in October, followed by a 3-1 win at Wembley Stadium in November.
If Real Madrid do decide to part ways with Zidane, it seems likely Pochettino will be a leading candidate to take over. Whether the Spurs boss will be tempted to move to the Bernabeu remains to be seen, but if Madrid make contact he may have a tough decision to make.