The Portuguese was in charge at Spurs early this season, when Hart eventually left the club for the Scottish giants.
He had wanted to remain at Spurs, after playing several games the season before under José Mourinho.
"There was a big change going on at Tottenham," Hart said on In The Stiffs podcast.
"They needed a lot of people out and a lot of people in, [Nuno Espirito Santo] proceeded to call me in.
"I knew they were signing another goalkeeper and I was like, 'do we need to have a conversation?'. He said that we'd speak after training.
"He was like, 'I'll speak first, let's be absolutely clear, no matter what happens, you'll not kick a ball this year'.
"I had got on really well at the club, people had bought into what I was trying to bring and I was like, 'right, okay'.
"He said, 'you'll be free to work with the sporting director to get yourself out, however you want to play it, play it'.
"I said just out of interest, remove yourself from the situation, you used to be a goalkeeper, why has it come to this?
"Why have I gone from being whoever I was to being completely surplus to requirements in a squad, to not even being able to back up the first-choice? Speak freely.
"He just went, 'in my opinion, we all reach a point in our career where the body won't allow you to play football. We're at it now. I would not feel comfortable with you playing one minute for me. The ball's too quick for you, you're too old, you're not moving, you've got no strength in your body'.
"He literally buried me and I'm laughing because, whether I'm deluded or not, I was like, I don't agree with any of that.
"I asked for your opinion, you have given it, it's not what I wanted to hear and I am going to have to take myself out of this situation.
"I literally went home and I am completely baffled here, I think I'm done, I can't be a***d anymore.
"I can't sit in a room anymore and have that said to me by him. Three years of literally not knowing what the hell I am doing.
"Going no direction just getting constantly volleyed in the face when all I am trying to do is my best.
"I was like: I don't need this anymore. I'm strong, I'm healthy, I love football.
"I went home and said I'd prefer to play 30 charity games a year for anyone who would want me to play in goal and give something back.
"I can't be a***d with chasing the ace. I like playing football, but I don't really like this anymore.
"Everyone who had my back couldn't really argue. They were like: I get what you are saying.
"I went back in the next day and said, the first bit, you are the manager, you make your decision. The rest of it was out of order.
"It's done. I'm not going to be a problem. I intend to train hard every day and find some sort of solution.
"It was just dealing with another problem for him. He's a manager and needed to clear wood. I was part of that wood.
"He made his decision and backed it. Good for him. He was the boss and I'm out.
"I got put in contact with Ange here. And I knew that Celtic had called anyway.
"They said we'd be okay with you talking to them, I was like, cheers.
"I've loved it, I've loved every minute of it. I'm really happy here."
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