Two of the most high-profile law-enforcement officials fired by President Donald Trump said Wednesday that Special Counsel Robert Mueller faces a high bar in proving criminal conduct in his investigation into possible collusion between the Trump campaign and Russia, addressing the possibility that he may not bring a case.

Sally Yates, the former acting attorney general, and Preet Bharara, the former Manhattan U.S. attorney, both emphasized in a joint interview Wednesday at Vanity Fair’s New Establishment Summit that Mr. Mueller’s...