And the left-back also admitted he held talks with Paris Saint-Germain a year before playing in the Champions League final.
Rose was a key member of Mauricio Pochettino's title-challenging Spurs side between 2015 and 2019.
He starred alongside Kyle Walker, Jan Vertonghen, Toby Alderweireld, as well as Kieran Trippier as the north London side battled for silverware.
At one point Rose was linked with a transfer to Manchester City at the height of his form.
But he has told talkSPORT there was the potential for an even more controversial inter-Premier League deal in 2017.
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Speaking on Drive, he said: "I spoke to a team across the river and I don't think I'd have been allowed back at Tottenham had that have materialised.
"I can't say it because I don't want to get them into trouble or anything but, yeah, had that have come up, I don't think the Tottenham fans would be singing my name like that anymore."
Speaking on potential regrets, he added: "I don't regret ever staying at Spurs. Possibly when I was once talking to one club, when Spurs found out I was speaking to this club they shut it down straight away.
"Sometimes I feel if I had been a bit stronger, because I've got that in me to be strong and say, 'No, this is what I want to do' sort of thing.
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"I sort of wonder, had I been like that, what may have been but in terms of other regrets, no not really. I loved my time at Spurs."
Rose also revealed in 2018 he was in touch with Paris Saint-Germain.
Speaking on transfers that could have materialised for him, he added: "Until a bid actually comes in, you don't know how close close is. But one of the big boys in France, I was close to going there.
"I spoke to Paris once upon a time. It was probably a year before the Champions League final, five years ago probably I spoke to them.
"I've spoken to teams in Italy and Turkey but as I said, until a bid actually comes in how close are you?"
Of Pochettino's flying full-backs it was Walker who left the club to sign for Manchester City.
When asked about if he would have left Spurs while they were challenging, he said: "Probably not but at the time, there were rumours that one full-back was allowed to leave, me or Kyle.
"I was told it's not going to be me basically, so yeah that decision was sort of taken away which at the time I wasn't angry about because you sort of hoped that Spurs were going somewhere so I didn't mind.
"But, coming back now and seeing how many trophies Kyle has collected you sort of do wonder sometimes."