Lorde, 17, is in the US ahead of a 16-date tour starting next month.
The Kiwi star angered Swift fans back in October when she said: "Taylor Swift is so flawless, and so unattainable, and I don't think it's breeding anything good in young girls".
But the pair have since become good friends and have been spotted together on a number of occasions, including hanging out together at the Grammy Awards.
Last week they spoke about a possible musical collaboration.