Swift, 23, and Styles, 18, started dating in November and spent the holidays together, but broke up after vacationing in the British Virgin Islands last week, the newspaper said.
No reason was given for the split.
People.com said representatives for the singers -- who are both scheduled to begin concert tours soon -- have not commented on the alleged end of their romance.
Styles is a member of the band One Direction.
Celebrity Families of 2014 [PHOTOS]