According to The Sun, the One Direction member has become "very close" with the Sinead O'Connor actress.
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"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.
