According to the Daily Mail, it's Perrie's hectic schedule with Little Mix that is the main factor, with a so-called source saying she didn't have the time to commit to a relationship right now.
The newspaper's insider said: "Perrie has called it off as she is so busy with Little Mix promo. She has the single out globally now at No.1 - and the album coming - followed by an international promo tour - then a US tour with Ariana Grande.
"In order to commit to someone at this busy time - she'd have to be really into them. It's a big commitment to date someone whilst you're constantly on the road - it's hard - and Perrie just wasn't really feeling things with Luke."
There's been no comment from either Perrie or Luke, who recently won over a new legion of fans thanks to his role alongside Michelle Keegan in BBC One's Our Girl.
They were always very private about their relationship, anyway.
Rumours of a budding romance surfaced back in August when a source claimed to have seem them enjoying a date in the West End watching a performance of musical Aladdin, before partying at Mahiki night club.
But it was only this month Perrie confirmed to The Sun: "We've been on a few fun dates, which is nice. It's very early days. It's early days but yeah, he's really lovely."
Bandmate Jesy Nelson added: "He's a lovely boy, nice boy."
Little Mix are currently promoting their new album Get Weird, which features track 'Shout Out To My Ex', which many have speculated could be directed towards Perrie's ex-fiance, former One Direction singer Zayn Malik.
Luke, meanwhile, has been filming the TV series Snatch alongside Harry Potter star Rupert Grint.