"We feel the future opportunities with the tabloids can be best exploited by a different ownership", the company said in a statement.
AMI has been in a legal quagmire for the past year due to Pecker's dealings with President Donald Trump and Michael Cohen.
American Media came under fire this year from Amazon founder Bezos for what he said were threats to publish explicit photos of him following a January story on him that included lurid texts exchanged with his mistress, former TV anchor Lauren Sanchez.
American Media LLC, the parent corporation of the National Enquirer, is "exploring strategic options" for the tabloid brand, according to its announcement. AMI has defended its reporting on Bezos' affair.
More recently, the National Enquirer has been embroiled in a battle with Bezos, who also owns the Washington Post.
Trump and his lawyers have argued the payments were a personal matter unrelated to the election.
After the sale, Pecker will continue to help manage The Enquirer through American Media Inc., which will remain under his leadership, the people said.
AMI's stable of titles that are not up for sale include Us Weekly, OK, Star, In Touch, Men's Journal, and Muscle & Fitness. A phone message seeking comment from Chatham was not immediately returned.
Prosecutors haven't reached a determination concerning the extortion claim, according to a person familiar with the investigation, and they are now working to examine another set of claims - those made last month by Bezos's security consultant, Gavin de Becker.
Elkan Abramowitz, an attorney who represents Pecker, defended AMI's chief executive and denied the allegations in a February 10 interview with ABC News Chief Anchor George Stephanopoulos on "This Week".
"Pecker didn't want to sell it, but he was forced to cut off his arm to save the rest of the company", one source close to the situation told The Post.