The 46-year-old had long been tipped to join the Spanish giants and succeed Zinedine Zidane, who resigned last week after the Champions League triumph over Liverpool.
Pochettino began his management career in Spain with Espanyol and returning to La Liga to take charge of Real Madrid is a tempting offer.
But the Daily Mail say the Argentine has ignored interest from Real in the knowledge that a move to the Spanish capital would provoke questions over his loyalty.
Pochettino has been at Tottenham since 2014 and committed his future to the club at the end of last month by signing a new five-year deal.
Despite failing to win a trophy, Spurs have shown improvement under Pochettinos watch and he is keen for their progress to continue over the coming years.
After signing a new five-year deal with the club, Pochettino said: I am honoured to have signed a new long-term contract as we approach one of the most significant periods in the clubs history and be the manager that will lead this team into our new world-class stadium.
This is just one of the factors that makes this one of the most exciting jobs in world football and we are already making plans to ensure we continue to build on the great work that everyone has contributed to over the past four years.[Chairman] Daniel [Levy] and I have spoken at length about our aspirations for this football club. We both share the same philosophies to achieve long-term, sustainable success.
This is a special club – we always strive to be creative in the way we work both on and off the pitch and will continue to stick to our principles in order to achieve the success this club deserves.
Levy added: We have been on an extraordinary journey and the times ahead look even more exciting as the club enters the next phase in its history.
Mauricio has fostered an incredible spirit in the team and has embraced a style of play our fans have loved watching. I know they will welcome this commitment by Mauricio.