Speaking of the romance, former U.S. Representative Patrick Kennedy told website TMZ: "We love Taylor Swift. She's been a great friend and we're happy for Conor.
"If she wants to be in the family, she's already a part of it."
Taylor - famed for writing songs about her romances with other celebrities - has spent lots of time with Conor over the last few months, even accompanying him to visit his mother's grave after she passed away in May.
She also missed him so much after having to leave him in Massachusetts to go to Nashville she chartered a private jet so he could visit.
A source said at the end of last month: "Taylor missed Conor so much, she sent a plane for him a few days later. He's been with her ever since, and his family doesn't know when he will be back.
"Things have become so serious between them so fast that no one in Hyannis Port [where the Kennedy family's summer home is located] would be surprised if they eloped."