The former So Solid Crew star was quoted as saying that "there was a relationship and attraction to each other's aura" between him and Cole.
Cole later denied the claims on Twitter, quipping: "Was this 'relationship' happening in your head @harveyofficial?! Are you smoking something ?"
MC Harvey has now told Choice FM that he and Cole "never kissed", adding: "I will 100% say that we had a communication relationship, but have I been out with her? No I haven't."
Of his ensuing Twitter war with Cole, he added: "I've never been with her, I've never claimed to have had a relationship with her, but the communication is not a lie.
"If I'd done that, I'd be lying to myself and lying to my family. If I'm saying, 'Was there communication with us?' Yes - for a good five months."
He suggested that he was surprised with how the interview was presented and added: "I was waiting for it to blow over, that's why I backed off. But when she publicly went and done that, she brought it to the forefront as a battle, and me personally, that's your fault.
"I didn't wanna go on a public social network and give people what they want and entertain it but naturally as a person, when you done that, you put me in a corner."
Of being quoted as saying that he would happily marry the Girls Aloud singer, MC Harvey said: "I did not say I would marry her."
It was claimed that Cole was planning legal action against Now magazine, who ran the initial interview, while the publication has stood by its initial report.
Earlier this week, email correspondence between MC Harvey and Cole were reportedly "verified" by media lawyer and legal advisor to Now, Tim Parish.
"I was asked to verify the authenticity of the emails between Cheryl Cole and Michael Harvey as a proof of a relationship between the couple," he said.