He was suspended as a Tory candidate on Tuesday, with the party saying that it had decided to take the action following its own internal inquiry.
Mr Williams issued a defiant statement in response, insisting that he had “committed a serious error of judgment, not an offence”.
Sky News reported the Gambling Commission team of interviews looking at his case includes two former police detectives and an ex-HMRC investigator.
It added that, if found to have broken the rules, he could face prosecution, a caution, or no further action depending on the evidence.
The Gambling Commission can investigate and prosecute breaches of the law, which can see those convicted face a fine or a jail sentence of up to two years.
Under the 2005 Gambling Act, it is a criminal offence to cheat at gambling yourself or to do anything for the purpose of enabling or assisting another person to cheat.
Mr Williams is one of five senior Tories who have been named as being under investigation by the gambling watchdog for bets on the timing of the election.
Laura Saunders, who was standing for the party in Bristol, is also being looked at and was suspended as a parliamentary candidate on Tuesday.