The 22-year-old singer and the One Direction heartthrob were seen holding hands at 'X Factor' rehearsals in the US last week, and Taylor was said to be so happy to see him she was like "a puppy dog".
The source said: "They lit up when they saw each other. Taylor was a puppy dog."
After watching her rehearse and sitting by her mother, Harry then took the 'I Knew You Were Trouble' singer to a backstage trailer in a particularly unusual manner - by carrying her.
The source added to Us Weekly magazine: "Harry picked her up and carried her to the trailer!"
Both have a colourful dating history, with Taylor previously being in relationships with actors Jake Gyllenhaal and Taylor Lautner and musician John Mayer, while Harry enjoyed a relationship with TV presenter Caroline Flack and was linked to singer Natalie Imbruglia.
However, a source said recently insisted Harry is determined to take things slowly with Taylor.
The source revealed: "Taylor and Harry have been quietly seeing each other again. When Taylor dates someone she jumps in full force, but Harry is being a little more cautious this time around.
"Taylor is a hopeless romantic, so she's really hoping it works out with Harry. Harry's being really sweet with her right now and careful not to hurt her."