AFAIK, the President can appoint a private citizen as a special envoy. According to Giuliani, the Ukrainians tried to reach out to the DOJ and FBI and they took no action.
I think you guys underestimate the responsibilities of the executive office.
The Special Envoy
AMONG all the instruments available to the President in his conduct of foreign relations, none is more flexible than the use of personal representatives. He is free to employ officials of the government or private citizens. He may give them such rank and title as seem appropriate to the tasks; these designations may be ambassador, commissioner, agent, delegate; or he may assign no title at all. He may send his agents to any place on earth that he thinks desirable and give them instructions either by word of mouth, or in writing, or through the Department of State, or in any other manner that seems to him fitted to the occasion. Some have been exceedingly formal; others completely informal.