"Get better soon Rudy, we will carry on!!!" Trump wrote Sunday on Twitter.
Giuliani has not announced his diagnosis. CNN has reached out to him for comment.
Giuliani has been traveling the country, leading the President's long-shot legal battle to overturn the results of the 2020 presidential election. He was mostly recently at the Georgia Capitol in Atlanta on Thursday to attend a Georgia state Senate hearing on the November election.
The 76-year-old former mayor of New York is considered at high risk for complications from the coronavirus due to his age.
Last month, Giuliani's son, Andrew, who is a White House staffer, tested positive for Covid-19 after attending a Trump campaign legal team news conference with his father in Washington, DC.
This story has been updated with additional information about Giuliani's recent travels.
