The millionaire businessman who campaigned and donated to the Brexit campaign is to appear before MPs on Tuesday to explain claims he held undisclosed meetings with Russian officials before the European Union referendum.
The paper said that Mr Banks and Leave.EU director of comunications Andy Wigmore had also had lunch with the ambassador in November 2016 - just three days after they and the former UKIP leader Nigel Farage had met Donald Trump in NY following his election victory.
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.
"Did that happen? Did he make money out of it and did he use that money to fund his campaigns?"
Banks had previously claimed in a book to have had only one meeting with Russian president Vladimir Putin's envoy in London, Alexander Yakovenko, in September 2015, but the newspaper said there were at least two further meetings.
Banks said he would appear before lawmakers later in the week and that he would tell them of his contacts with officials from other countries too.
"This is big news, because if the Russian government is seeking to develop relationships with prominent people like Arron Banks - not just a wealthy businessman but someone who's been the biggest private funder of political campaigns in this country, whose funding of Leave.EU played a central role in the build-up to the Brexit referendum and the referendum itself - I think we have a right to know what the level of that contact was, particularly when Mr Banks has sought to deny that", he told BBC1's Sunday Politics.
"I had two boozy lunches with the Russian ambassador and another cup of tea with him".
They were also said to have met Alexander Udod, one of 23 suspected Russian intelligence officers ejected from the United Kingdom after the poisoning of Sergei and Yulia Skripal in Salisbury.
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Supporters of Brexit say pro-Europeans are trying to undermine the referendum result with baseless allegations of Russian involvement so that they can push for a rerun of the vote.
The emails were given to The Sunday Times by journalist Isabel Oakeshott, Mr Banks's ghostwriter on The Bad Boys of Brexit. "Bite me. It's a convenient political witch-hunt, both over Brexit and Trump".
He told the paper that nothing had come of their discussions over the goldmine deal.
"We didn't profit from any business deals because I never pursued anything", said Mr Banks, who has interests in South African diamond mining.
The Observer claimed the emails suggested Mr Banks visited Moscow in February 2016 to meet key partners and financiers behind a gold project, including a Russian bank.
Ms Oakeshott wrote in the newspaper that Mr Banks and Mr Wigmore were "shamelessly used by the Russians".
"When foreign powers are aggressively targeting the values, systems and institutions upon which our democracy is built, then it's absolutely essential that we have regulatory, security and intelligence-based organisations who are ready, willing and able to intervene", Kinnock said.
The paper quoted Andy Wigmore, a close associate of Banks who was present at the meeting, as saying that they did not offer "any information to (the ambassador) or any Russian any details of our campaign".