The pair was out to catch a show by rock band Haim, at the Troubadour in West Hollywood on Thursday, reported People magazine.
Rumours of Swift, 25, dating Harris, 31, surfaced last Thursday when they were spotted showing affection for each other at Kenny Chesney's Nashville concert - where the "Shake It Off" singer made a surprise onstage appearance.
Both musicians are no strangers to dating people in the public eye.
Swift has had high-profile romances with Harry Styles, Jake Gyllenhaal and John Mayer.
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