Police Commander Victor Joseph reportedly sent an e-mail on Wednesday ordering Major Crimes investigators to bring full uniforms and combat uniforms to work for the time being.
In the local media's internal note, Joseph said, "There is a belief" fired, and "big" protests are expected in the central business district within 24 hours if it happens.
"The protest would be semi-spontaneous and most likely short-term," the memo said. "Based on this information, tomorrow, 19 April 2018, all Major Crimes detectives will be required to bring a full uniform and any protective equipment (combat equipment) to work until further notice."
Preparation is a precautionary measure
The Pittsburgh Police refused to comment further. CNN did not independently receive a copy of the memo.
In a statement, Pittsburgh Public Safety Director Wendell Hissrich said urban police officers value and prepare such situations as a precautionary measure.
"We regularly receive information about possible events and / or threats, assess the credibility of the information and plan for a potential event," Hissrich said.
"In that case, we have not assessed the credibility of the potential for interference, and we are unaware of the president's decision-making process."
A group in Pittsburgh has demanded a rally "No one is above the law" when Mueller is dismissed, but it is unclear whether the police response based on it.
Trump: "They are still here"
Trump downplayed speculation on Wednesday that he wanted to dismiss Mueller or Deputy Minister of Justice Rod Rosenstein, who directs the investigation.
"They said I'll get rid of them in the last three months, four months, five months, and they're still here," the president told reporters.
Speculation about Mueller's fate grew after the FBI ransacked the house, office and hotel room last week by Trump's personal lawyer Michael Cohen.
Since then, the president has openly argued about firing Mueller and reiterated his attack on the investigator's investigation as a "witch hunt". Trump is also contemplating trimming Rosenstein to limit Müller's investigation, several individuals familiar with the discussions told CNN.
His boss, Attorney General Jeff Sessions, apologized for investigating issues related to the presidential campaign.
CNN's Dave Alsup contributed to this report.