The 25-year-old "Shake It Off" hitmaker and the Scottish DJ were spotted holding hands together during their outing, reported Ace Showbiz.
In two photos posted by a fan, Swift and Harris were seen wearing similar tone outfits. The "Blank Space" songstress sported a long-sleeved dark grey tee, a black skater skirt and black boots.
She tied her hair in low ponytail and carried a black handbag.
The 31-year-old music producer, meanwhile, wore a short-sleeved dark grey tee, black pants and a pair of sneakers. He was seen carrying a shopping bag.
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In the second photo, the rumoured couple was seen walking side-by-side at a parking lot.
Swift and Harris dating rumours first emerged last week after she, Selena Gomez, Ellie Goulding and HAIM headed to Las Vegas to watch the DJ's performance at Hakkasan nightclub.
Harris allegedly sent a private jet for Taylor and the girls to fly them from NYC to Las Vegas.