Spurs had initially hoped to relocate into their new permanent home early this season, but construction delays have kept them at Wembley, which they also used throughout the 2017-18 campaign.
The situation was particularly frustrating for the club and supporters when a home Carabao Cup tie against Watford back in September had to be played in Milton Keynes due to another event taking place at the national stadium.
Pochettino said in November last year that he hoped a February move-in date was possible, and although that proved to be an impossibility, the Spurs boss appears to have confirmed reports that the switch is imminent.
Spurs beat Borussia Dortmund 1-0 in Germany to progress 4-0 on aggregate, and Pochettino is hopeful their next opponents will be the first to play at the new stadium in European competition.
"I expect yes, to play in the new stadium, of course," Pochettino told reporters. "We were talking yesterday with Daniel [Levy, club chairman] and he was very positive.
"I hope, yes, and my wish is to play there. Before the game we were listening to the song of the Champions League and we were talking with Jesus [Perez, Pochettino's assistant], saying it will be amazing standing in the new stadium and hear that song before the game.
"Now we are in the quarter-finals, hope we can finish [the stadium] and we can listen to the song there."
Tuesday's win saw Spurs secure a place in the last eight of the competition for the first time since 2010-11, but Pochettino was quick to quash any suggestion of this being evidence of them reaching the so-called "next level".
"For me, to move to the next level or the last level, I think it's not only today to show a very professional performance," Pochettino added.
"It's so important to be in the quarter-final, but you need to show more if you want to be at the next level.
"To build that possibility to be at the same level as the clubs that we are talking about, you need to start from the first step always.
"We are in the middle or 70 per cent of moving forward. I think we are working hard to one day be there. I think the stadium is going to be an important step for the club."