Lawyers for Michael T. Flynn, President Trump’s former national security adviser, notified the president’s legal team in recent days that they could no longer discuss the special counsel’s investigation, according to four people involved in the case, an indication that Mr. Flynn is cooperating with prosecutors or negotiating such a deal.

Mr. Flynn’s lawyers had been sharing information with Mr. Trump’s lawyers about the investigation by the special counsel, Robert S. Mueller III, who is examining whether anyone around Mr. Trump was involved in Russian efforts to undermine Hillary Clinton’s presidential campaign.

That agreement has been terminated, the four people said. Defense lawyers frequently share information during investigations, but they must stop when doing so would pose a conflict of interest. It is unethical for lawyers to work together when one client is cooperating with prosecutors and another is still under investigation.