Giuliani became known as “America’s Mayor” after leading New York City through the aftermath of the 9/11 attacks.
After the 2020 presidential election, Giuliani and other advisers traveled across the country accusing Trump’s opponent – former President Joe Biden – of attempting to steal the election and making false claims about the results.
Later, a jury forced him to pay two election workers whom he had accused of ballot fraud $148m (£108m) for defamation.
“Mayor Giuliani is a fighter who has faced every challenge in his life with unwavering strength, and he’s fighting with that same level of strength as we speak,” Goodman said in the social media post.
He added: “We do ask that you join us in prayer for America’s Mayor Rudy Giuliani.”
Last September, Giuliani, who will turn 82 this month, was a passenger in a Ford Bronco when it was struck from behind in the US state of New Hampshire.
He suffered a fractured thoracic vertebrae, multiple lacerations and contusions, and injuries to his left arm and lower leg, his security guard said at the time.