Taylor Swift's New Beau: Conor Kennedy?

The pair, who have been spending lots of time together, "walked out hand-in-hand" after having pizza recently

Photo: WENN

Oops, wrong Kennedy!

Over the Fourth of July, Taylor Swift was photographed hugging Patrick Schwarzenegger, Maria Shriver’s son. But now it appears that Conor Kennedy, the son of Robert Kennedy Jr. and the late Mary Kennedy, is actually Taylor’s love interest. He is pictured just to the right of Swift in the same photo – and the two have been spending lots of time together.

On July 25, Swift, 22, and Kennedy, 18, enjoyed slices at Kennedy family favorite Marcella’s Pizza in his hometown, Mount Kisco, N.Y., and “walked out hand-in-hand,” according to a source. Earlier that day, Kennedy was appointed as the administrator of his late mom’s $2.1 million-plus estate, according to the Boston Herald.

Days later, the pair grabbed pizza again and visited with his grandmother, Ethel Kennedy. And on July 29, they lunched with friends at Baxter’s on Cape Cod where she ate chicken fingers and sat next to Kennedy. Swift “was smiling a lot and she looked happy,” says an observer.

The New York Post also reports that the couple were seen kissing and holding hands over the weekend.

Swift has been open about her love for all things Kennedy. She said she was “starstruck” when she met Caroline and Ethel in January, and has called Jackie Kennedy a style inspiration.

And the Kennedy’s seem to admire the Grammy-winning country star as well. On Dec. 3, Swift will be honored by the Robert F. Kennedy Center for Justice and Human Rights for her commitment to social change, especially her work against bullying and LGBT discrimination. Ethel Kennedy will present the award.

For more on Swift and Kennedy – including photos of their time in Hyannisport – check out this week’s issue of PEOPLE, on newsstands Friday

• Reporting by KEVIN O’DONNELL and SYDNEY BERGER