Michael Cohen, Donald Trump’s former personal lawyer who is under federal investigation, bought a $6.7 million apartment in April in a new Manhattan skyscraper that is being developed by two of Mr. Trump’s longtime friends, according to people familiar with the transaction.

Located at 111 Murray Street in Manhattan’s Tribeca neighborhood, the project is being developed by a partnership of real estate companies Fisher Brothers, Witkoff and New Valley. New Valley is headed by Howard Lorber, a real estate developer and longtime...