The 'Gotta Be You' star is said to have kissed the X Factor singer backstage at a show and the pair were spotted "getting cosy" again during filming of the video for charity single 'Wishing On A Star'.
Malik's bandmate Niall Horan has also apparently become "obsessed" with Edwards and sources suggest that the 18-year-old will be devastated by the new romance.
"Zayn has got in there first but Niall is obsessed with her too," a source told The Sun.
"They met her on the video shoot and have both been trying to win her over. They plan to come out as a couple after The X Factor has finished."
Malik split with his X Factor co-star Rebecca Ferguson back in July after a four-month relationship.
Ferguson recently said that the break-up taught her "a great big lesson" about finding love in the spotlight.
> Little Mix: 'We don't get much attention from boys'
Watch Little Mix and One Direction perform 'Wishing On A Star' on The X Factor below: