It started out as nothing more than a thought bubble on a TV show – Andrew Bolt on Channel Ten’s The Project on Tuesday night, talking about the need for a new conservative party following Prime Minister Malcolm Turnbull’s ascension to the throne.

Waleed Aly half-jokingly suggested “the Bernardi party”, to which Bolt replied that the South Australian Liberal senator was one person worth looking at to deliver on the idea.

Reports of plans for a breakaway conservative party made headlines the next day, with Senator Bernardi choosing not to comment, which only fanned the media speculation.

• Bernardi an ‘embarrassment’
• Andrew Bolt suggests new party
• Nova Peris: Bolt should go

A spokesperson from his office emailed The New Daily saying: “Senator Bernardi has no comment to make in relation to any suggestion by Waleed Aly.”

Senator Bernardi was publicly opposed to the dumping of former Prime Minister Abbott, and on the pews within the Liberal Party’s broad church, he sits at the opposite end to the moderate new PM in Malcolm Turnbull.

If he does want to abandon ship, Senator Bernardi doesn’t have to worry about starting a whole new party – Family First senator Bob Day would love to poach him, although he thinks his fellow South Australian religious conservative may be of more use where he is.

“Whilst Family First would obviously welcome Senator Bernardi with open arms, he is serving a very important purpose as the conscience of the Liberal Party,” his office told The New Daily in an email.

Family First wouldn’t just welcome Liberal party senators with “open arms” – the party is reaching out to Liberal voters too, particularly those suspicious of Mr Turnbull’s well-publicised personal support for marriage equality.

Hours after Mr Turnbull had taken the prime ministership from Mr Abbott, Mr Day released a statement putting forward the party as an alternative option for “traditional” Liberal voters.

“Australia still has a political party that represents traditional marriage, family values, disciplined spending and lower taxes,” he said.

“In my home state of South Australia, there is the opportunity now for voters to shift their vote.

“If traditional Liberal voters want somewhere to go, Family First would welcome them with open arms.”

As it stands, Mr Turnbull has not adjusted the Coalition government’s existing policy on same-sex marriage – repeatedly affirming this week that the policy remains to hold a plebiscite on the issue after the next election.

That has done little to dampen speculation that conservative senators such as Senator Bernardi might wish to look for a new home.

On Thursday social media lit up with claims that the Senator had removed the name of the Liberal Party from his Twitter handle as a form of protest against the dumping of Mr Abbott.

Cory Bernardi has removed the Liberal Party from his Twitter bio and is now a “Conservative Senator” #auspol pic.twitter.com/AacRsQPYnL

— Dean Sherr (@deansherr) September 17, 2015

Senator Bernardi quickly hosed down the chatter by tweeting out that he hadn’t edited his Twitter handle in months.

For those in press, you know I hate to disappoint but nothing has changed on my Twitter bio for many, many months. Much ado about nothing. — Cory Bernardi (@corybernardi) September 17, 2015

Yet on talk of defecting from the party he has steadfastly represented in the Senate for nearly a decade, Senator Bernardi’s only comment is “no comment”.