A $150,000 payment to Ms McDougal was made by the then-publisher of the supermarket tabloid National Enquirer, which kept her story from coming to light.
Mr Trump was also invited to testify.
Manhattan District Attorney Alvin Bragg’s office has apparently been examining whether any state laws were broken in connection with the payments or the way Mr Trump’s company compensated Mr Cohen for his work to keep the women’s allegations quiet.
Mr Trump, 76, denies the encounters occurred, says he did nothing wrong and has cast the investigation as a “witch hunt” by a Democratic prosecutor bent on sabotaging the Republican’s 2024 presidential campaign.
Mr Cohen pleaded guilty, served prison time and was disbarred. Federal prosecutors never charged Mr Trump with any crime.
Mr Trump’s attorney, Joe Tacopina, told NBC News that the former president will follow normal procedures if it gets to the point of having to surrender to authorities from the District Attorney’s office.
If Mr Trump’s claims are true, it would make him the first former president ever to face criminal charges.