Mr. Trump’s advisers asserted that the debate commission included “anti-Trumpers.” They also complained about previous moderators, Mr. Fahrenkopf said.

Mr. Fahrenkopf, in turn, insisted that the debate commission did not include any anti-Trump bias, and he said he walked Mr. Parscale through the guidelines for commission board members that require their neutrality.

He also said that with one exception, the commission did not think any of the moderators chosen over several decades had exhibited concerning behavior during the debates…

Since then, Mr. Parscale has told people that he was investigating other options for hosting the debates. It is not clear which outside firms he or other officials are talking to, and the campaign declined to provide any details.