Michael Cohen, President Trump’s former lawyer, has met multiple times with special counsel Robert Mueller’s investigators, including within the past month, according to people familiar with the matter.

As part of the meetings, investigators asked Mr. Cohen questions about Mr. Trump, including about the president’s business dealings with Russia, one of the people said. Mr. Cohen’s lawyer had previously said his client was open to meeting with Mr. Mueller but it wasn’t clear the special counsel would want to do so.

Mr....