It has sparked a string of damaging headlines about Cohen and how Trump's lawyer and so-called fixer sought payments from companies following Trump's 2016 election, apparently for consulting work - including AT&T and pharma giant Novartis.
"Within approximately 75 days of the payment to Ms. Clifford, Mr. Viktor Vekselberg, a Russian oligarch with close ties to Russian President Vladimir Putin, caused substantial funds to be deposited into the bank account from which Mr. Cohen made the payment".
US President Donald Trump officially admitted on Thursday for the first time that he repaid his former personal lawyer up to $250,000 (€210,000), but did not explicitly say what the reimbursement was for.
Al-Rumaihi told the Post that Mr Cohen made the solicitation in early December at the Peninsula Hotel in NY, an account Mr Siegfried confirmed.
Mr Trump previously denied knowing of the $130,000 payment to Stormy Daniels.
During an interview on MSNBC's "Morning Joe," attorney Michael Avenatti said he is in talks with two women who allege they have agreements with either Trump or his personal lawyer, Michael Cohen, to stay quiet about an affair with the president.
The Office of Government Ethics, which oversees the financial-disclosure documents, said in its own footnote that it had concluded Trump had to report the payment to Cohen in a section that detailed Trump's legal liabilities over the course of 2017 and the first half of 2018. It says Trump "fully reimbursed Mr. Cohen in 2017".
Last year, the attorneys general of the District of Columbia and Maryland sued Trump over the issue.
In one of his less-than-savvy moves, Cohen used this same shell company to pay off adult film star Stormy Daniels, who alleged she had an affair with Trump.
The hush-money payment to Daniels is reportedly a focus of a federal investigation into Cohen's private finances and business interests.
Novartis has faced public outrage in recent weeks over its payment to Essential Consultants, a company founded by Mr. Cohen in 2016.
Giuliani said he knew news of the payment would come out, even if he didn't know "exactly when or what would come out".
Cohen's discussions with Sater about the Trump Tower Moscow ended then, according to Yahoo News, but Sater said he continued working on a potential deal through December 2016, stopping only after Trump had been elected.
Editor's note, May 17, 2:20 p.m.: In a statement, a spokesperson for Al-Rumaihi wrote, "In December 2016, Ahmed Al-Rumaihi and Michael Cohen met to discuss a potential Qatari investment in USA infrastructure by Qatar Investments, which is a division of the Qatar Investment Authority ("QIA")".