The 18-year-old pop star is dating the 'We Are Never Ever Getting Back Together' singer and wants her to perform with him and the rest of the boy band - Niall Horan, Louis Tomlinson, Liam Payne and Zayn Malik - to a crowd of 20,000 fans, reported Daily Mirror online.
Little Mix's Perrie Edwards, 19, is flying out to the US with her mother to join boyfriend Malik and Tomlinson has invited his girlfriend Eleanor Calder along for the show as well.
"It is such a momentous time for the boys and they want their girlfriends by their sides. Seeing Zayn with Perrie and Louis with Eleanor made Harry realise there's a person he wants to be there with him, too. Taylor," a source said.
Styles has recently opened up about his feelings for Swift and praised her for being a sweet person.
"Taylor honestly couldn't be a sweeter person. She is genuinely nice and extremely talented, and she deserves everything she has," he said.
Swift, who has previously been in relationships with Jake Gyllenhaal, John Mayer and Taylor Lautner, has just come back to US from Australia where she performed at the ARIA Awards.