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CLOSE ENOUGH: Jack Black impersonating Romney.

CLOSE ENOUGH: Jack Black impersonating Romney. (CBS)

JOKE’S ON YOU: Mitt Romney visits David Letterman on the “Late Show” on March 2, 2010. He says he hasn’t been on lately because of scheduling. (
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Despite the apparent bitterness, there’s been “constant contact” between David Letterman’s “Late Show” and the Mitt Romney campaign, says the show’s executive producer.

“We’re in constant contact with the Romney team, inviting them on to the show on a regular basis, but they have not accepted our offer,” Rob Burnett told The Post.

“They’re saying it’s all about scheduling — they’re not ruling out an appearance, but until they’re here, they’re not here.”

Since winning the Republican presidential nomination, Romney has refused to appear on “Late Show” — and Letterman has turned this into a running gag.

“I don’t see us stopping anytime soon,” says Burnett, who’s also CEO of Letterman’s Worldwide Pants production company. “We come up with the best, funniest things we can come up with every day — and, right now, Mitt Romney seems to be an excellent source of comedy for us.”

Letterman has told his viewers not to vote for Romney unless he appears on the show — and, Tuesday night, conducted a “simulated” interview with “Mitt Romney,” who was played by slovenly comic actor Jack Black.

“Any misgivings I previously had in talking to you have been vanquished!” Black/Romney told Letterman — adding that he regretted “my ill-advised decision to delay my appearance on your program.”

The kerfuffle started when, in the now-infamous “47 percent” video, Romney said Letterman “hates” him because he’s appeared on rival Jay Leno’s “Tonight Show” many times.

Letterman says that’s not true, and after Romney’s remarks surfaced, he’s repeatedly invited Romney and his wife, Ann, onto “Late Show” — but has thus far been spurned.

(Romney has appeared on “Late Show” three times but not since last December, when he presented the show’s “Top 10” list. Since being elected, President Obama has twice appeared on the show.)

“I can’t speak for Romney, but there’s no animosity, no enmity, from our side,” Burnett says. “We’d love to have Gov. Romney on. He’d be welcomed here. I don’t know how to say it any clearer.”

Burnett says he understands that Romney’s been busy the past few days prepping for last night’s first debate with President Obama in Colorado.

“But I find it hard to believe that there’s not a way to find an hour somewhere, in the next 34 days, to come over here and spend some time with us,” he says.

“You can’t expect to be elected president of the United States without sitting next to Dave first.”

Romney officials had no comment yesterday.