It's rumoured the 24-year-old American songstress recently began dating the British rock star, who is the lead vocalist for Manchester-based band The 1975.
But apparently Taylor isn't interested in pursuing anything serious with Matt right now.
"It's very new and they're having fun," a source told Us Weekly magazine. "They're seeing where things go."
It's claimed Taylor and Matt exchanged phone numbers at his band's Los Angeles concert in October.
Taylor has previously dated stars including Jake Gyllenhaal, John Mayer and One Direction's Harry Styles. Her past love affairs were highly publicised and she became the bud of many jokes. Tina Fey and Amy Poehler even took a swipe at Taylor's romantic life while they hosted the Golden Globes last year.
Taylor previously lamented to Us about the way her personal affairs were portrayed in the media.
"It broke my heart!" she said. "I was selling out stadiums and it was all people talked about."
In a recent interview with Billboard magazine, the Shake It Off singer insisted she is more than happy not being in a relationship.
'I, however, am 24, perfectly happy being alone, and one of the reasons I'm perfectly happy being alone is that no one gets hurt this way,' Taylor noted.
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