People Magazine reports that the country star has been spotted out and about with Connor Kennedy, son of Robert Kennedy Jr., several times in the past week.
The publication says that Taylor was seen eating pizza with Conor in Mount Kisco, New York, and quotes an unnamed source as saying the couple "walked out hand-in-hand".
People goes on to say that the couple lunched with friends at the weekend in Cape Cod and quotes another source as saying the Story Of Us singer "was smiling a lot and she looked happy".
Picture agency WENN has since obtained snaps of the pair enjoying a sailboat ride during their romantic weekend together at the Kennedy family compound in Hyannisport, Massachusetts.
Swift has also been spending time with Conor's cousin, Patrick Schwarzenegger, who is the son of movie star Arnold.
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