Donald Trump’s longtime personal lawyer has claimed the US president knew in advance of a June 2016 meeting in which Russians were expected to offer “dirt” on election rival Hillary Clinton, according to US media reports.

The assertion by Michael Cohen, reported by both CNN and NBC News, contradicts Trump’s insistence that he was unaware of the meeting at Trump Tower in New York, the subject of huge controversy once it came to light a year later.

Cohen is prepared to make a statement to Robert Mueller, who is investigating alleged collusion between the Trump campaign and Russia in the 2016 presidential election, the networks said.

Trump’s son Don Jr, son-in-law Jared Kushner and campaign chairman Paul Manafort met at Trump Tower on 9 June 2016 with the Russian lawyer Natalia Veselnitskaya, having been told she was offering sensitive information about Clinton from the Russian government.

Trump, his son, his lawyers and other officials have repeatedly claimed the future president did not know about the meeting until details of it were revealed in July last year.

The president told reporters onboard Air Force One at the time: “I only heard about it two or three days ago.”

On Thursday, CNN, citing an unnamed source, reported that Cohen says he was present when Don Jr told his father about the Russians’ offer to meet and that Trump approved it. NBC said it had independently verified the report.

Trump’s current lawyer, Rudy Giuliani, dismissed Cohen as lacking credibility. “It would have to be people in the room with the president that can corroborate Cohen, which there won’t be because it didn’t happen,” he told CNN. “And then it becomes a credibility contest between two or three witnesses who say one thing and Cohen who says another.”

He added of Cohen: “He’s been lying all week, he’s been lying for years” – a comment potentially damaging to Trump since Cohen was working for him during those years.

Once unswervingly loyal to Trump, Cohen has fallen out with the president in recent months. On Tuesday, CNN broadcast a taped conversation between him and Trump discussing how to hush up allegations that Trump had an affair with Playboy model Karen McDougal in 2006.

Cohen is under federal investigation in New York for his business dealings. The leaked tape fuelled speculation over whether he is considering a co-operation deal with prosecutors. Cohen does not have an audio recording to back his claim about the Trump Tower meeting, the reports said.

The June 2016 meeting was brokered by a British music promoter, Rob Goldstone, who contacted Trump Jr saying he had “official documents and information that would incriminate Hillary and her dealings with Russia and would be very useful to your father”.

He added: “This is obviously very high level and sensitive information but is part of Russia and its government’s support for Mr Trump ... I can also send this info to your father.”

Trump Jr responded “I love it” when first offered this political “dirt” on Clinton, the Democratic presidential candidate, but he has since contended that no meaningful information was offered and the meeting focused mostly on the issue of adoptions of Russian children.

The Associated Press reported on Thursday that Veselnitskaya, the lawyer who met with Trump Jr, “worked more closely with senior Russian government officials than she previously let on”.

Mueller has indicted 31 individuals, including 12 Russian intelligence agents, for hacking computer networks of the Democrats. Trump has repeatedly denounced the investigation as a “rigged witch-hunt” and was widely criticised for appearing to side with Vladimir Putin over his own intelligence agencies at a joint press conference in Helsinki earlier this month.