Supermodel Christie Brinkley, who has been squired by singer-songwriter John Mellencamp since September, opened up Wednesday about her new beau.

Speaking with People magazine, Brinkley, 62, says that when she met the 64-year-old Grammy Award-winner last year, “I thought, ‘Oh my gosh, we’re really opposites. He’s kind of a throwback from another time, like a silent cowboy.’ But then we talked and realized that we do have a lot of shared interests.”

One of them, she told the magazine, was being parents and, in Mellencamp’s case, a grandparent. Brinkley has a daughter with her second ex-husband Billy Joel, singer Alexa Ray Joel, 30; a son, Jack Paris Brinkley Taubman, 21, with her third ex-husband, real estate developer Ricky Taubman; and a daughter, Sailor Lee Brinkley Cook, who turned 18 on July 2, with her fourth ex-husband, architect Peter Cook. Mellencamp has five children from three marriages, and six grandchildren.

Another thing they have bonded over, she said, was age-appropriateness. “I know guys that go out with girls that are so, so young,” Brinkley said. “They’ll throw some reference out, and they’re like, ‘What’s that?’,” adding, “When it comes to relationships, there is something nice about just being the same age.”

She played down rumors she and Mellencamp may be planning to marry, but conceded, “You never really know what’s going to happen.” She added: “John and I are two people that have very full lives. We’re just trying to enjoy each other when we can see each other and try not to put too much on it.”

Brinkley, who additionally has a lucrative career as a beauty-care entrepreneur and author, said she recognizes that, “It is kind of a special thing to be 62 and have so many opportunities,” and that, “I never take that for granted, not for a second.”

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Brinkley made headlines on Independence Day when she entered into a social-media war after turning a garden hose on a woman she says urinated on her beachfront property at Sag Harbor Cove.

The full interview, excerpted online, appears in the new issue of People.