According to The Sun, the One Direction member has become "very close" with the Sinead O'Connor actress.
"She's in the fame game too so she understands what it's like to have people interested in her private life. They're very sweet together," a source claimed.
However, Mailk denied the rumours on Twitter, telling a follower: "no I don't have a gf , x (sic)"
The 'What Makes You Beautiful' singer split with fellow X Factor star Rebecca Ferguson in July.
The star, 18, recently denied rumours alleging that he had a fling with Cher Lloyd.