The couple have been dating for the last six months, but Jaric says he was perplexed by a Web-based rumor about his checking out the local jewelry store for the big stone.
"I am not shopping right now," Jaric, 29, tells PEOPLE. "But I could start tomorrow. I am that close. I'm definitely not yet engaged, but it doesn't mean we're not thinking about it."
At that point, the entire process may come as a surprise. "I would rather keep that my own secret," says Jaric. "It's a life decision ... a private thing."
The stoic Serb admits he's not normally romantic, but being with the Brazilian supermodel, 26, has changed him. "I was not the person to fall in love easily. I am a difficult person from that standpoint," he says. "Now, it's a little different situation."
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