The Electoral Commission referred him to the National Crime Agency (NCA) on Thursday, saying that it had grounds to believe that he was not the source of the money.
Challenged by Marr to explain where the money for his Brexit campaign came from, the millionaire businessman and self-style "bad boy of Brexit" again denied it came from overseas, saying instead it originated from his own United Kingdom businesses.
His funding of the Brexit campaign has been dubbed the biggest donation in British political history.
Banks is being investigated by the National Crime Agency (NCA) after his case was referred to it by the Electoral Commission, which said there were reasonable grounds to suspect Banks was "not the true source" of £8mn given to the Leave.EU campaign.
Liberal Democrat Brexit spokesman Tom Brake said Mr Banks' appearance on the Andrew Marr Show had been "remarkable".
Mr Banks, who's denied any wrongdoing, insisted there was no Russian money and no interference of any kind - declaring the money came from a UK-based limited company, which he owned.
It said that loans to the parent company and received on behalf of Leave.EU may have involved a non-UK listed company, Rock Holdings, which is incorporated in the Isle of Man.
Repeating his allegation of a political motive to the investigation into himself and Leave.EU, Mr Banks disagreed the UK's exit from the EU should be postponed until the NCA probe is completed.
"For Rock Services to have money to give to Leave.EU or anyone else, that money has got to have been put in that bank account by another company or another individual".
Mr Banks said Rock Services has "all sorts of revenues" but did not detail them.
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"It's a group of vicious MPs who have grouped together with the Guardian and the FT".
'It means that if I had my time again I think we would have been better to probably remain and not unleash these demons, ' he told Mr Marr.
He told Sky News: The £8m came from a United Kingdom company, the cash was generated in the UK.
One of the leading figures behind Britain's decision to leave the European Union now says he would vote for the United Kingdom to remain, claiming it would have been better to "not unleash these demons" created by Brexit.
Leave campaigner Arron Banks appeared on the Andrew Marr show on Sunday morning.
When pressed further, he said: "Goodbye, I'm not talking to you".
Mr Banks revealed he had seconded a small number of people to run a call centre in Bristol but stressed this was properly declared to the Electoral Commission. Asked why he had written to Mr Collins's constituents in Folkestone and Hythe, calling him a "snake in the grass", Mr Banks replied: "Well, he is".
"Channel 4 are a propaganda channel", Mr Banks responded.
On Tuesday, the Information Commissioner, Elizabeth Denham, will announce the outcome of an inquiry into claims Eldon shared customer data obtained for insurance purposes with Leave.EU, potentially breaking data protection laws.