But in an e-mailed statement on Monday, Giuliani changed his story, saying: "My comments did not represent the actual timing or circumstances of any such discussions".
He concluded by saying the Moscow project "was in the earliest stage and did not advance beyond a free non-binding letter of intent".
The Kremlin was not engaged in any discussions regarding the potential construction of a Trump Tower skyscraper in Moscow, even though it received several emails regarding the matter, Kremlin spokesman Dmitry Peskov has stated.
When Cohen pleaded guilty to a charge from Mueller's office in November, he said had he lied about the duration of the proposed Moscow project. Saying that the talks ended in January 2016 was a lie, Cohen admitted.
"Absolutely", Giuliani said about if he's anxious that lying for Trump will stain his legacy.
BuzzFeed also reported Cohen had told the special counsel about Trump's instructions to lie to Congress and that documents and witness testimony would support Cohen's statements. He echoed Kremlin talking points on key foreign policy topics like the ongoing conflict in Ukraine, the usefulness of the North Atlantic Treaty Organisation alliance and the fight against ISIS in Syria.
Cohen, who found himself in Mueller's crosshairs, has already been sentenced to three years in prison for campaign finance violations, tax evasion and lying to Congress regarding Trump's business dealings in Russian Federation prior to the Trump presidency.
In fact, he later admitted, they had gone on much longer, until June of 2016, when Trump had become the presumptive nominee of the Republican party. Trump publicly encouraged the Russians to hack Hillary Clinton's private server, though he later said he was joking.
"I never said there was no collusion between the campaign or people in the campaign", Giuliani said on Cuomo Prime Time.
Cohen reportedly said that the talks had come to an end in January 2016, while the negotiations were allegedly underway at least in the middle of 2016, the height of the presidential campaign.
"It's our understanding that [the discussions] went on throughout 2016", Mr Giuliani, a former New York City mayor, told NBC's Meet the Press program.
"Probably up to, could be up to as far as October, November", he said. "So any time during that period, they could have talked about it", he said. The BuzzFeed report took things a step further by alleging that Trump told Cohen to lie in September 2017.