Under his leadership, Spurs have claimed three top-three finishes in his four years in charge, with the north London club just two points behind second-placed Manchester City in 2018-19.
The Argentine has been strongly linked with the permanent post at Old Trafford, but Pochettino says he's focused on his job at Tottenham in both the short and long term.
"I hope, or I wish, to be here 20 years, and decide to leave or to finish my career here," Pochettino said.
"I am so focused here, and want to help the club to achieve what the club want to be in history."
He added: "It would be fantastic. I am so happy to be here. I am so happy to work in that pressure. Why not?"
Santiago Solari replaced Julen Lopetegui just a few weeks into the Spanish Liga campaign, while Ole Gunnar Solskjaer has taken over for Jose Mourinho for the rest of the Premier League season.
And while Pochettino's name continues to be mentioned as a possible option for United and Madrid, he says he hopes to replicate the longevity of former rival Arsene Wenger, who remained boss of Arsenal for 22 years.
"But I don't know because I need to ask [Wenger] one day, if I have the possibility, if he is happy in the way that he finished," Pochettino said. "What I saw from my point of view, it was so unfair how the people treated him."