According to The Sun, country singer Taylor fell "head over heels" for the curly-haired heartthrob after meeting backstage while touring the US - but was crushed when photos of Harry kissing another girl surfaced.
The paper claims that the first Swift knew of the snaps were texts from Harry begging for a chance to explain.
She is rumoured to have trawled the internet, where she found the pictures of Styles with 18-year-old model Emma Ostilly in New Zealand.
A source told The Sun: "Taylor really liked Harry and he hinted at making it official with her.
"She had her love goggles on and didn't care what anybody had to say about him. She was heartbroken."
The paper reports that the 1D singer's spokesman declined to comment on the story.
In other Harry news, that curly mop could soon be a thing of the past.
Appearing on Channel 4's Freshly Squeezed, the 18-year-old was asked whether he would consider shaving his head for charity.
And Styles replied: "Yes, I would. If I raised enough money then yeah... for Children In Need."
Harry recently confessed that he was keen to get a new do but was banned from losing his famous locks.
He told Radio 1's Nick Grimshaw: "I want to shave my hair off and no one will really let me. Everyone's telling me not to do it.
"My argument is, like, I think my popularity is in my face, and not my hair."