Mr Williams, who was the Tory MP for Montgomery until the election was called and is standing again in the new constituency of Montgomeryshire and Glyndwr, previously apologised and said he made a “huge error of judgement”.
When asked by the BBC, he refused to say whether he placed a bet on the basis of inside information.
Following the latest allegation, a Conservative spokesman said: “As instructed by the Gambling Commission, we are not permitted to discuss any matters related to any investigation with the subject or any other persons.”
Last week, Mr Sunak said he had been “incredibly angry” to learn about the allegations, promising to “boot out” anyone found to have broken gambling laws from the Conservative Party.
Mr Sunak announced 4 July as the date of the general election on 22 May, taking much of Westminster by surprise.
If someone uses confidential information to gain an unfair advantage when betting, this could be a criminal offence under section 42 of the Gambling Act.
A spokesperson for the Gambling Commission previously confirmed to the BBC it is “investigating the possibility of offences concerning the date of the election”.
The Commission also said it could not provide any further details about the investigation or who was being looked into as it is an ongoing process.
“We are not confirming or denying the identity of any individuals involved in this investigation”, it said.
Labour and the Liberal Democrats have both previously called for Ms Saunders and Mr Williams to be suspended as Conservative candidates.
On Saturday night, the Liberal Democrats again called for Prime Minister Mr Sunak to suspend everyone under investigation.
The party’s Deputy Leader Daisy Cooper said the PM must launch a Cabinet Office inquiry into the reports, which she described as an “all-out scandal at the heart of the Conservative Party”.
“People are sick and tired of this sleaze. Day by day, hour by hour, the Conservative Government mire themselves in more of it”, she said.
Housing Secretary Mr Gove has condemned the latest reports, and likened the controversy to Partygate during the Covid-19 crisis.
“It looks like one rule for them and one rule for us,” the Tory cabinet minister, who is not standing again at the election, told the Sunday Times.
Labour have not yet responded to these latest allegations, but the party’s leader Sir Keir Starmer has previously said anyone accused of similar conduct in his ranks would “be gone and their feet would not have touched the floor”.
It has also emerged that a police officer working as part of the prime minister’s close protection team had been arrested following an allegation of bets on the timing of the election.
The officer was initially suspended by the Metropolitan Police and then arrested on suspicion of misconduct in public office.
The individual has been bailed pending further inquiries.
The Met was contacted by the Gambling Commission last Friday. It informed the force that it was investigating alleged bets made by a police constable from the Met’s Royalty and Specialist Protection Command.