The Little Mix singer and Luke were first romantically linked back in August, but reports had claimed the pair cooled things off just weeks after their first date.
However, rumour now has it that Perrie and Luke are back on and they are "taking things slow."
According to The Mirror, a source told the publication that things are not yet serious between Perrie and Luke - as he is concentrating on his acting career.
They claimed: "They have decided to keep their romance off social media and stay private for a while as they get to know each other. Luke wants to take things slow with Perrie and just date, he is really focused on his career."
Although, neither Perrie and Luke have actually addressed the latest dating rumours. Perrie had reportedly confirmed to The Mirror that things were "going well" between them last month at V Festival, but a source had recently told Reveal that Luke has "made it known" he and Perrie are not together.
"He's been laughing at the rumours," the source said. "And was overheard telling people they're just friends and have never been a couple."
Reveal has contacted reps for both Luke and Perrie for comment.
Fans may recognise Luke from Skins - he played the role of Freddie back in 2008 - and he is currently starring alongside Michelle Keegan in Our Girl as her ex-fiancé Elvis.
Rumours he is dating Perrie come after she split from former One Direction star Zayn Malik in August last year. They had dated for four years and announced their engagement in 2013, before Zayn decided to call time on their relationship.
It was claimed he had dumped Perrie via text message, but Zayn later set the record straight, insisting he hadn't. In an interview with Fader magazine, Zayn explained: "I have more respect for Perrie than to end anything over text message. I love her a lot, and I always will, and I would never end our relationship over four years like that. She knows that, I know that, and the public should know that as well."
Zayn is now dating model Gigi Hadid.
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