Photos surfaced showing the two young stars wearing matching necklaces on separate occasions, reported Aceshowbiz.
The rumor first emerged after Swift and Styles met at 2012 Kids' Choice Awards last summer before she dated Conor Kennedy.
She was reportedly left heartbroken after being dumped by the One Direction member and poured her heart out in one of her songs in new album "Red".
In an interview, Styles, 18, had said he and 22-year-old Swift swapped phone numbers but insisted there was nothing romantic between them.
"We met in America, she's very nice. We're friends," he had said.
Swift was previously linked to Joe Jonas, Taylor Lautner, Jake Gyllenhaal, Chord Overstreet and John Mayer.
