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 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.
Both Labour and the Liberal Democrats called for Mr Sunak to suspend those under investigation.
Labour’s shadow education secretary Bridget Phillipson described the allegations as “pretty shocking” and said there would be “genuine disgust” amongst voters.
Liberal Democrat deputy leader Daisy Cooper said the PM should 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 Michael 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.