Spurs currently sit fourth in the standings but are just a point behind third-placed Liverpool and have a game in hand on the Merseysiders.
United currently occupy second position, six points clear of Spurs, while both teams only have three league matches left to play in their respective campaigns.
It would certainly be a long shot if Spurs, who will round their campaign off with an away clash against West Brom and home games with Newcastle and Leicester, were able to overhaul United in the standings, but Pochettino is not giving up hope.
"It is not up to us. In our hands to finish third because we have one game more than Liverpool," Pochettino told reporters. "We need to win the three games but we have to wait for Manchester United to lose.
"All can happen in football, which is why it is such an amazing sport."
Even if Spurs ended up finishing fourth in the top flight they would still qualify for next season's Champions League courtesy of Arsenal's exit from the Europa League on Thursday.
Pochettino believes that would represent success for the north Londoners although he never likes to benefit from another team's misfortune.
"I am not happy about it or enjoy it when another team loses, but of course it is for our interests," the 46-year-old added. "I think to finish in the top four is a massive success for the club."