In the last few days, Trump has acknowledged that he reimbursed Cohen for the Dollars 130,000 he paid to Daniels.
Within 75 days, Mr Avenatti said, Mr Viktor Vekselberg - a Russian oligarch with links to Russian President Vladimir Putin - "caused substantial funds to be deposited into the bank account, from which Cohen made the payment" to Ms Daniels.
Vekselberg is the chairman of Renova, a Russian investment company. He (Cohen) made payments for the president or he's conducted business for the president'.
Though originally noting Avenatti "provided no documentation for his claims", NBC News was also able to "review financial documents that appear to support" the attorney.
Taken together, the Times' reporting and Avenatti's document offer the most detailed picture to date on Cohen's business dealings and financial entanglements in the run-up to and aftermath of the election.
Separately, federal prosecutors in Manhattan are investigating the payment and Mr Cohen's broader business practices.
Cohen, Trump's longtime personal lawyer, faces a criminal investigation in part over the payment to Daniels.
"Mr. Vekselberg and his cousin Mr. Andrew Intrater routed eight payments to Mr. Cohen through a company named Columbus Nova LLC ("Columbus") beginning in January 2017 and continuing until at least August 2017", states Avenatti's report. The former New York City mayor said the payments were made in multiple installments. Novartis - whose chief executive was among 15 business leaders invited to dinner with Trump at the World Economic Forum in January - spent more than $10 million on lobbying in Washington past year and frequently seeks approvals from federal drug regulators.
Cohen and his attorney did not immediately respond to requests for comment.
The other companies were Novartis AG, AT&T and Korea Aerospace Industries Ltd.
Don't miss: Will U.S. Go to War with Iran? First Republic declined to comment.
Larry Solomon, a spokesman for AT&T, confirmed the relationship with the firm in an email on Tuesday.
AT&T spokeswoman Megan Ketterer said in a written statement: "Essential Consultants was one of several firms we engaged in early 2017 to provide insights into understanding the new administration".