The Argentine manager also jokingly abstained from questions over his past links with the Manchester United job.
Pochettino was announced as the head coach of the United States men's national team in September after a one-year spell at Chelsea.
His Stamford Bridge tenure followed a five-and-a-half season stint at Spurs, during which he competed for two Premier League titles.
Fans chanted his name towards the end of Antonio Conte's dramatic reign in 2023, and it is clear the club is still close to Pochettino's heart.
Reflecting on his surprise Spurs exit in 2019 on talkSPORT Drive, he said: "To be honest, the day that I left the club always I was thinking one day to come back.
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"It's not that I was thinking before the offer from the USA national team, I was thinking to come back.
"The day that I left I was thinking I would love to one day come back to Tottenham because like I told in the past, I said for me, I felt empty in the moment that I left.
"It was like an unfinished job and that is why. It's a feeling, it's a feeling, it's a dream.
"I don't know how you can take or I can explain or describe but I think for sure it's a club that is always going to be special for me.
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"And I would like to one day to have the possibility again to try to arrive in a situation that we are back to finish in a different way."
Pochettino is no stranger to the Premier League given his experience with Southampton, Spurs and Chelsea.
He is considered one of the top coaches around, and Man United were famously linked with his services on more than one occasion.
The 53-year-old was a target before Erik ten Hag took charge in 2022, with talkSPORT also reporting his interest in the job following his Chelsea exit last summer.
talkSPORT Drive presenter and avid United fan Andy Goldstein was keen to know more on the rumours, but was left disappointed.
He asked: "One final question, and if you answer it I will send you a bowl of lemons… I'm a Manchester United fan, how close were you to managing my club?"
Pochettino responded: "Okay. Thank you very much! I will send my address."
Goldstein replied: "Do you not want the lemons?
"How close? Was there a conversation? That's my last question. Was there a conversation at one stage?"
Pretending to not understand the question, Pochettino responded: "Sorry, sorry, sorry. If I, sorry?"
Goldstein continued: "I was just asking, was there a conversation with United at any stage for you to take over there?"
But Pochettino didn't back down from his jokey response and said: "I don't… I cannot hear!"
Pochettino has already taken charge of the USMNT on six occasions, with wins coming in five of those matches.
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He looks set to manage the United States when they host the 2026 World Cup alongside Canada and Mexico.
However, his attention will currently be focused on the upcoming international break when they face Panama in the CONCACAF Nations League semi-finals on March 20.
Mauricio Pochettino has pundits in stitches with 'big balls' comment about USMNT player