The pair was photographed talking to a fan at a Whole Foods on Wednesday while wearing matching ensembles.
The alleged couple was also seen holding hands as they left Kenny Chesney's concert Thursday, where Swift was a guest performer. Attendees claim the pair were seen holding hands and kissing during the show.
Sources told Us Weekly Swift, 25, is in Nashville rehearsing for her forthcoming 1989 World Tour and that Harris traveled to Music City to see her.
The "Blank Space" singer and Harris, the world's highest paid DJ, were also seen together backstage at the 2015 Brit Awards in February.