The pair were rumoured to be dating last year, shortly before Little Mix won The X Factor UK.
She was said to have dumped her boyfriend for Malik, but later ended her relationship with the boyband singer to focus on her career.
However, their relationship is back on and they were spotted watching Avengers Assemble at the cinema earlier this week, The Sun reports.
A source said: "They've always been very close and have kept in touch during 1D's tour. Now Zayn is back they are going to be a proper item - even though it's going to be a bit of a long-distance relationship at times."
After the cinema visit, Edwards tweeted: "Just went to see avengers assemble and it was #boring. Good night though! xD @zaynmalik."
Malik wrote in response: "@PerrieLittleMix yeah tonight was fun lets do it again sometime ;) x x."
Meanwhile, Harry Styles has apparently reunited with childhood sweetheart Felicity Skinner after returning home to Cheshire during One Direction's two-week break.
He took her out for dinner on Thursday night (April 26) at the restaurant Gusto in Alderley Edge.