Arie Luyendyk Jr. & Lauren Burnham Have 'Talked About Running Away to Vegas' to Elope

The former race car driver only just proposed to runner-up Burnham on Tuesday’s After the Final Rose special — which came after breaking off his engagement with Becca Kufrin on Monday’s dramatic season 22 finale — but wedding plans are already in the works.

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“We want to get married soon, and we also talked about eloping,” Burnham, 26, told reporters during a teleconference on Wednesday, as Luyendyk Jr., 36, added, “We’ve talked about running away to Vegas.”

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If they end up opting for a more traditional wedding, Burnham said she she’s not “picky” about the details, though there’s a few things they both have in mind for it.

“We’re talking about an evening wedding or a sunset wedding,” Luyendyk Jr. said. “Lighting is important. Lots of flowers.”

He added: “We talked a little bit about maybe doing a TV wedding if that works with our timeline.”

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Though Luyendyk Jr. said he wouldn’t mind Burnham inviting friends from the show to the wedding, there’s one person he doesn’t want to see on the list — “Becca, she’s not invited,” he said.

Moments after proposing to Burnham with a 3.5 carat Neil Lane ring on the conclusion of the two-part finale on Tuesday, Luyendyk Jr. told PEOPLE, “We’re so ready for this.”

“Lauren told me I’m four months late on this proposal, and I wanted to give it to her and I wanted everyone at home to share in it,” he continued.

For her part, Burnham said she “had an inkling” about the proposal. “Arie’s not good at keeping secrets,” she said. “He didn’t tell me, but he gave me hints!”

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Luyendyk Jr. and Burnham said their wedding will happen this year. Next, Burnham will move to Scottsdale to be with her fiancée and is planning on working in real estate with him.

“We’re both very excited about marriage and starting a family,” Burnham tells PEOPLE in this week’s cover issue.

In fact, Luyendyk Jr. says he wants two to four kids: “If we get lucky, maybe we’d have twins!”