While holding a campaign rally in Florida in the early hours of the day, Trump took issue with the media coverage of the COVID-19 pandemic, prompting the crowd to chant "Fire Fauci".
"Don't tell anybody but let me wait until a little bit after the election", Trump replied, as quoted by CNN, thanking his supporters for the advice.
A video of the moment has been circulating in social media.
It's been reported that the US president has plans to purge several people from his cabinet if he wins the 3 November presidential election. Fauci, a member of the White House Coronavirus Task Force, is known to have differences with the president over the country's handling of the pandemic.
The United States remains the country with the highest number of registered coronavirus cases (over 9.28 million) and the highest COVID-19 death toll (more than 231,000).