July 6, 2012 at 11:23 AM ET
Flirt alert! Taylor Swift, 22, spent Independence Day hanging out with Patrick Schwarzenegger, 18, at the Kennedy compound in Hyannis Port, Mass., a source tells Us Weekly. "They are getting to know each other, but she thinks he's cute!"
The "Both of Us" singer had been invited to celebrate the national holiday with the political family and several friends, including Glee star Dianna Agron, 26. "She is close with the whole family," the source explains of Swift.
As for Swift and Schwarzenegger? "They are getting to know each other. We will see! But she didn't go there just for him."
After sailing in the afternoon July 3, Swift, Agron and the Kennedys -- including Robert Jr., Ethel, Ted and Rory -- spent time on the beach, "playing capture the flag and tag," according to an onlooker, who adds that "they had a bonfire."
"Taylor was taking photos of everyone with a huge camera and Dianna took one of Taylor with Patrick together," the onlooker tells Us. "He kept kicking sand at her and was flirty with her."
Schwarzenegger -- whose mother, Maria Shriver, is the daughter of the late politician Sargent Shriver and his late wife, Eunice Kennedy Shriver -- tweeted that the holiday was "the best 4th of July I could ask for. Hope everyone had a great day!"