The paper said he and Mr Wigmore also had lunch with the ambassador in November 2016, three days after they and Mr Farage had met Donald Trump in NY following his victory in the United States presidential election.
Mr Banks said he will be reporting the "theft" on Tuesday.
Banks co-founded the Leave.EU campaign that is credited with mobilizing grassroots support for Brexit.
The Sunday Times said Mr Banks and Mr Wigmore were introduced to Ambassador Alexander Yakovenko by a suspected Russian spy - since expelled from Britain after the Salisbury poisoning case.
The ambassador was said to have proposed a business deal that would have involved them in the consolidation into one company of six Russian gold mines.
Banks' snub comes after the communications chief of Vote Leave, which won official designation as the lead Brexit campaign group ahead of Leave.EU, also refused to appear, prompting Britain's parliament to take the rare step of ordering him to come.
There are no suggestions of criminal wrongdoing.
But Banks dismissed the claims, telling the paper: "I had two boozy lunches with the Russian ambassador and another cup of tea with him".
"It's a convenient political witch-hunt, both over Brexit and Trump".
Banks also told the paper nothing came of the gold mine discussions.
"We didn't profit from any business deals because I never pursued anything", he said.
The businessman, whose wife is Russian, said he made a "family trip" to Moscow in February 2016 but "no meetings were had with anyone".
The Russian embassy has said it has not intervened in United Kingdom domestic politics.
Mr Wigmore insisted he and Mr Banks never any Russians information about their Brexit campaign.
The emails were given to The Sunday Times by journalist Isabel Oakeshott, Mr Banks's ghostwriter on The Bad Boys of Brexit.
The Leave.EU founder said he has Russian visas in his passport showing he went to the country in 2014 and 2015 to visit his Russian in-laws, but not February 2016, four months before the Brexit vote.
Committee chairman Damian Collins, a Conservative MP, said the latest reports raised serious questions about possible Russian interference in United Kingdom politics.
"At the moment what we know is he had more meetings than he let on". "Was that money made used in political campaigning?"
In late may, Russian President Vladimir Putin called nonsense the assertion that Russia could intervene in adoption in the United Kingdom of the decision to withdraw this country from the European Union. It does it in a variety of ways. "Yeah, we had two lunches with the Russian ambassador and passed on a business contact".
At a press conference at the conclusion of the G7 summit in the canadian resort of La Malbaie in the province of Quebec to the Prime Minister of the UK Theresa may was asked whether she believed that British security services should investigate the revelation in the article that the head of the government said: "I have not seen the publication in The Sunday Times, but I think that any recognition of the need of the investigation and the competent authorities, it will".
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