The rapper explained on Twitter that he initially tried to tease the media by inventing a scandalous fake response to false claims that he had split with the Made in Chelsea star.
"Publicist got an e mail from the daily star asking why me and millie had broken up," he wrote.
"She replied saying it wasn't true...despite my best efforts to get her to tell them we had, and it was because millie was having a relationship with a bird behind me back."
He added later: "No, it isn't true that millie was seeing a bird behind my back, that's just what i wanted to tell the paper that asked if we'd broken up."
Green previously accused the press of "prejudice" in regard to his relationship with Mackintosh, saying: "People are so quick to point out the difference in class.
"If the difference were race people wouldn't be so quick to point it out - it's still prejudice isn't it? I find it weird that's it such a big thing."
The couple were first reported to be dating back in February.