David Perel, the editorial director of In Touch and Life & Style at Bauer Publishing, is said to be under pressure some two years after the former editor-in-chief of the National Enquirer and Radar Online joined the weekly celebrity magazines.

Supplying the heat are slumping newsstand sales coupled with a libel and defamation suit filed against In Touch by country singer Blake Shelton.

“With its In Touch cover, ‘Rehab for Blake,’ Bauer crossed the line,” claims Shelton’s lawsuit filed in a Los Angeles court.

“The defamatory, but surely well-selling, cover portrayed Shelton as in rehab or on his way there,” the suit contends. “Inside, Bauer told a slightly different, albeit no less false and defamatory story about a boozy, irresponsible womanizer who needed an intervention and rehab to avoid ending up dead. Nothing could be further from the truth,” the court papers claim. “Shelton was not in rehab and has never been to rehab, considered going to rehab or been urged by his friends, colleagues and team to go to rehab.”

Bauer is asking the court to toss the suit because Shelton has not established actual malice.

“Shelton cannot establish a probability of prevailing on his libel claim because the statements identified in the complaint are substantially true, non-defamatory or protected opinion and thus non-actionable,” claims Bauer.

The two sides are due back in court on March 28.

Perel’s boss, Bauer CEO Hubert Boehle, was already unhappy with the company’s titles’ plunging newsstand sales, sources said.

In Touch’s total circulation dropped 14.2 percent in the six months ended Dec. 31, according to the Alliance for Audited Media. Life & Style dropped 10.6 percent in the same period.

Both titles missed their rate base — which is the circulation level that they promise advertisers they will deliver each week — in the second half of 2015.

Despite rumblings that Perel is under the gun, a Bauer spokeswoman insisted the rumor was “complete BS.”