Before he pleaded guilty and began assisting federal prosecutors last summer, Michael D. Cohen, President Trump’s former fixer, spoke with a lawyer who agreed to reach out to the president’s legal team on his behalf.

The lawyer, Robert J. Costello, had about a dozen conversations with Mr. Trump’s lead lawyer, Rudolph W. Giuliani, according to emails and documents reviewed by The New York Times and interviews with people involved in the matter. In one email, the discussions were characterized as a “back channel of communication.”

During one of the conversations last April, Mr. Costello said in an interview, he asked whether Mr. Trump might put a pardon “on the table” for Mr. Cohen, who was under federal investigation for a variety of possible crimes, including arranging hush-money payments to two women who had said they had affairs with Mr. Trump. Mr. Giuliani told Mr. Costello that the president was unwilling to discuss pardons at that time, Mr. Costello said in the interview, and they did not discuss it again.

Now federal prosecutors have requested the emails and documents from Mr. Costello, according to a copy of the request, which cited an investigation into “possible violations of federal criminal law” but offered no further detail. The request, sent last week, was for any documents related to Mr. Cohen as well as any bills Mr. Costello had sent him.