The ex-Northern Ireland international lives on one side of Capaldi’s home in west Glasgow with ex-Rangers player Andy Halliday living on the other.
The revelation emerged during a humorous exchange on Clyde 1 radio station during which the Forget Me singer was asked how he leaves the house.
“It’s alright, I live with a bunch of old people – I moved into an old folk’s home,” he quipped.
"No – the people I live around aren’t really big fans of my music.”
The 26-year-old star then revealed he has rubbed his famous neighbour up the wrong way on more than one occasion.
"Mr Lennon – I parked in his space a couple of times and I got notes on my car door,” Capaldi explained.
"So if you’re listening Neil I apologise.
"Don’t leave notes on my car – just ask me to move it and I’ll move it.”
Capaldi changed his parking habits in a bid to keep the peace with his neighbour, but ended up annoying another resident.
"And then I parked it in another space where I live and then I got like this woman [who] wrote, and I don’t know if it was a woman but if it’s the woman I think it is who lives in the house,” he explained.
“I don’t know because they never put their flat number on it because they are a coward.
“But basically said: ‘Ok, you are blocking the way blah, blah, blah, blah, blah – also, I hope you never need an ambulance in a hurry’.
"I was like what!?
"That is a threat on my life.”
It comes after Capaldi overtook Ed Sheeran with the UK’s most streamed song ever.
Someone You Loved topped Sheeran’s Shape Of You in a list compiled to celebrate 70 years of the Official Singles Chart.
It gained 562million audio and video streams.
Capaldi hailed himself “king of music” after receiving an award and an inflatable crown from the Official Charts Company.
After joking that “nice guys finish last” he praised Sheeran, who has co-written with him, as being “like a brother” and a “mentor”.