Styles, 19, and Swift, 22, who split earlier this year, are said to have rekindled their romance, reported Sun online.
Styles has invited Swift to a party in New York which will also be attended by his parents.
"He has been very hush-hush about Taylor but this is the perfect chance to introduce her to them," a source said.
Styles and Swift had separated after the former was caught kissing a model.
The young Brit recently even joined Swift's mother as he sat in the audience to watch her perform on the US X Factor.
Swift has been previously linked to Joe Jonas, Taylor Lautner, Jake Gyllenhaal, Chord Overstreet, John Mayer and Conor Kennedy.
