The prime minister made his surprise election announcement on 22 May.
Mr Jack said in a statement: “I had no knowledge of the date of the election until the day it was called.
“I placed no bets in May and am not under investigation by the Gambling Commission.”
A spokesperson for the Gambling Commission said: “We are not confirming or denying the identity of any individuals involved in this investigation.”
Alister Jack had been telling colleagues and journalists for at least a year that he thought a June or July election made the most strategic sense for his party.
He has represented Scotland in the UK cabinet since 2019, under the premierships of Boris Johnson, Liz Truss and Rishi Sunak.
His controversial decision in 2021 to block the Scottish government’s gender self-ID reforms was seen as a significant moment in the demise of Nicola Sturgeon’s period as Scotland’s First Minister.
In February 2024, he expressed “regret” after deleting all of his WhatsApp messages from during the pandemic.
He said he erased his files to free up storage capacity on his phone in November 2021.