But he decided not to pursue the deal, and said the context of the meetings in 2015 and 2016 was different to now, when Britain's relations with Russia have suffered after Britain accused it of being behind a nerve agent attack on a former Russian spy in England three months ago.
According to details of emails reported by the Sunday Times and the Observer, Mr Banks and Mr Wigmore also discussed potential business opportunities in Russian Federation including a proposal involving six gold mines.
As they were not MPs, he said he and Mr Banks were not required to officially record who they met but he said he would give MPs details of all their meetings, including with Central Intelligence Agency officers in the USA embassy in London.
"Where's the evidence we took Russian money?"
Mr Banks appeared in front of the Media Committee after it was claimed the Leave.EU co-founder had been involved in a conspiracy with Russian officials ahead of the Brexit vote.
The businessman sat alongside Leave.EU communications chief Andy Wigmore as they joined Nigel Farage for an exclusive LBC interview.
"I was told a certain time and we've got a lunch appointment we don't want to be late for".
Mr Banks told MPs that no money from his overseas business interests formed part of his political donations and he was "crystal clear" about the rules.
'But I think we've been as open as we could be with the issues you've raised'. "I thought it was interesting", Banks said, referring to the meeting.
"I'm not going to be lectured about my business interests".
"Clearly that's nonsense", he said. Lunch with the Russian ambassador?
Meanwhile, Mr Wigmore told MPs he initially met Russian officials at a UKIP conference to talk about bananas in his role as a diplomat for Belize and had since met Russian figures "many times".
Mr Banks, whose wife is Russian, said opponents of Brexit and Mr Trump had seized on claims of Russian interference as an explanation for their defeats, suggesting several MPs had used the ancient right of parliamentary privilege to accuse Leave.EU in the House of Commons.
Cambridge Analytica, which was hired by Trump in 2016, has denied its work on the USA president's successful election campaign made use of allegedly improperly harvested data - but questions have since been raised over any role in other votes. "The ambassador was probably in a worse state than we were", he said.
Asked to stay a further five minutes to conclude questioning Mr Banks insisted he had to leave, adding he had been "as open as can be" about claims suggesting an inappropriate relationship with Russian Federation.
Thiem, Nadal in French Open final
Earlier, Thiem needed to survive a nasty bout of the jitters to see off Marco Cecchinato and reach his first grand slam final. But it took Muguruza quite a while to get going against Halep, who managed to keep sending ball after ball back over the net.