Federal authorities have subpoenaed the publisher of the National Enquirer for records related to its $150,000 payment to a former Playboy model for the rights to her story alleging an affair with Donald Trump, according to people familiar with the matter.

The subpoena from Manhattan federal prosecutors requesting information from the publisher, American Media Inc., about its August 2016 payment to Karen McDougal is part of a broader criminal investigation of Mr. Trump’s former personal lawyer, Michael Cohen, they said.

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