Michael Avenatti, Daniels' lawyer, also said that Trump and Cohen should immediately release bank statements that could shed light on a series of payments made to Cohen's shell company.
"This is an enormous amount of money," Avenatti said on MSNBC's "Morning Joe" show.
"You've got millions of dollars that are ... being deposited into this account," Avenatti said. "Michael Cohen appears to be selling access to the president of the United States."
Later Wednesday, a senior official at Swiss pharmaceuticals giant Novartis told NBC News that Cohen had reached out to Novartis shortly after Trump's election "promising access" to the new administration. Cohen and his attorney did not respond to a request for comment to NBC News.
White House press secretary Sarah Huckabee Sanders, when asked Wednesday if Trump was worried about major corporations paying his lawyer, said, "I haven't heard the president expressed any specific concerns about that."
An estimated $4.4 million or more has been identified as flowing through Cohen's shell company, Essential Consultants, which was created in October 2016, a month before Trump's election, according to a report by Avenatti's firm.
Cohen said Wednesday that Avenatti's "document is inaccurate," according to NBC News. He did not elaborate on what was supposedly wrong about the document.