The country singer and the `Tron: Legacy` actor are allegedly getting close after they met up for a low-key date in Nashville, where Taylor is currently recording.
A source said: "It was their first time going out. They`ve been emailing for a while, and she hinted they should get together.
"She has actually spent time getting to know Garrett. He`s cute - and he`s into country music! [She] likes that he`s a normal guy."
The 26-year-old hunk - who also starred in `Country Strong`, playing an up and coming country singer - joined Taylor at a restaurant at 8.00pm before returning to his hotel at 12.30am.
The `You Belong With Me` star`s romantic life has been varied of late, with the 21-year-old blonde breaking up with Jake Gyllenhaal last year, before being linked to `Glee` star Chord Overstreet. She has also dated musicians Joe Jonas and Jon Mayer.