"Michael Cohen should cooperate with the government," Giuliani added. "We have no reason to believe he did anything wrong. The president did nothing wrong with him."
Asked if he had any concerns about what Cohen might tell a prosecutor, Giuliani said, "Zero. None."
"As long as he tells the truth ... we're home free," said Giuliani, who is currently representing the president in connection with a probe of the Trump campaign by special counsel Robert Mueller.
That investigation, which is focused on Russian interference in the 2016 presidential election and possible collusion with that effort by the Trump campaign, is separate from the probe of Cohen. Trump has repeatedly denied there was any collusion and has called Mueller's investigation a "witch hunt."
Davis declined to comment Monday when contacted by CNBC about his tweet referring to Trump and Giuliani.
Davis referred questions to Petrillo, who did not immediately respond to a request for comment.
Cohen has not been charged with any crime. The investigation is related to his business dealings as well as to a $130,000 payment he made to porn star Stormy Daniels on the eve of the presidential election, in which Trump defeated Hillary Clinton.
Daniels has said the payment was in exchange for her silence about a sexual encounter she had with Trump in 2006. The White House has denied any such affair. But Trump has admitted he reimbursed Cohen for his hush money payment to Daniels.