Are modesty ponchos and chaste coverups coming to the Sports Illustrated Swimsuit Issue?

Multiple sources tell Page Six that the annual annals of female anatomy is facing a sticky situation after Sports Illustrated was purchased by the wholesome Midwestern folks at Meredith along with other Time Inc. publications.

Plus there are further concerns the bikini bonanza could hit a bum note following the #MeToo movement.

We’re told that SI staffers are mulling what the purchase by the Iowa-based publisher — whose far less racy titles have names like Family Circle, Family Fun and Midwest Living — could mean for the swimsuit flesh fest.

Corporate insiders tells us that the publisher — which bought Time for its more on-brand titles like People and Real Simple — is hoping to off-load Sports Illustrated as soon as possible, so the Swimsuit Issue issue could be moot.

But with editors already thinking about next year’s edition of the franchise — which has been a cash cow for Time Inc. — and a quick sale not guaranteed, staff are wondering what a Meredith-produced breast fest might look like.

“If you look at Meredith,” said a source, “what it stands for and what is in the their lineup, a swimsuit issue is a bit off the grid. Showing [frequent star] Nina Agdal’s sandy butt [or Kate Upton in yet another way-too-small top] is not usually the direction they’d go in.”

Meanwhile, despite female staffers’ protests, Time Inc. had continued a long-running tradition of showing off the issue by handing out copies to every lucky Time employee. In 2008, an employee complained about finding “under my door . . . a beautifully laid-out publication of porn. Who decided I wanted to look at 100-some pages of barely dressed girls with abs made of slate and boobs that defy reason?” “Can’t imagine that will survive the #MeToo era,” added another source.

Even before Meredith took the reins in February, Time Inc. had been trying to rebrand the issue as empowering for women, with limited success. Sports Illustrated reps didn’t get back to us.