Government Services Minister Bill Shorten says Scott Morrison should be embarrassed by the Robodebt royal commission but it is up to the former prime minister to decide if he should quit parliament.

It comes amid a split in the Coalition over Mr Morrison’s reaction to the royal commission’s scathing report – and conflicting reports that at least one of the former PM’s favourite titles is under threat.

The Cronulla Sharks are reportedly considering cancelling Mr Morrison’s No.1 ticketholder status amid the ongoing scrutiny of his role in the robo-debt scheme.

The Sydney Morning Herald reported an official from the NRL club, which gave the former PM the honorary title in 2016, had confirmed Mr Morrison would likely to be dumped it he was found guilty of any negligence or wrongdoing.

However, a spokesperson for Mr Morrison said his office had contacted Sharks management and had been told the story was inaccurate.

The disagreement came as Mr Morrison faced fresh calls to resign from parliament because of his role in the failed debt recovery scheme as uncovered by a royal commission into the government program.

It found former Coalition ministers, including Mr Morrison, dismissed or ignored concerns about the legality of the scheme.

Mr Morrison has rejected suggestions of wrongdoing or that he misled cabinet.

On Monday, Mr Shorten told ABC radio it was up to Mr Morrison to stay and “protest his innocence” if he wished.

“That’s up to him, but anyone who reads the royal commission is going to form a different view about Mr Morrison’s proposed timetable for staying in parliament,” Mr Shorten said.

He said any “self-respecting politician” would be “embarrassed, humiliated” by the assessments in the final report.

“He must live in a separate world to the rest of us,” he said.

Meanwhile, Liberal backbencher Bridget Archer has told the Nine newspapers she was disappointed by Mr Morrison’s response to the report’s findings.

“He was very quick to reject the findings of the royal commission rather than seek to engage constructively with its findings and find ways to reform the system to ensure this doesn’t ever happen again,” she said.

“I would like to see self-reflection from the people involved in creating this scheme because of the harm and damage it has caused to people and the continued erosion of trust in public institutions it has created.”

The outspoken Tasmanian MP said it was difficult for a former prime minister to remain in parliament.

“This, alongside other things, do make it difficult for the party to draw a line under the past and move forward,” she said.

Nationals leader David Littleproud said Mr Morrison, who represents the Sydney seat of Cook, needed to decide if he was still set on serving in federal parliament.

“It’s a matter for Mr Morrison to determine whether he’s still got the heart to continue on,” Mr Littleproud told Sky News on Monday.

“If he hasn’t, then he should get out of the road, because the people of Cook deserve someone that has the fire in the belly to stand up and to represent them in Canberra.

“He’s paid the ultimate price in losing his job as the prime minister of this country.”

It emerged on Monday that the Liberal Party has started preselection for all of its NSW seats – except Cook, suggesting Mr Morrison may resign before the next election.

Opposition home affairs spokesman James Paterson said the Liberal Party was not in a position to direct Mr Morrison to “say or do anything”.

“What he decides to do with his future is a matter for him,” he told ABC radio.

Senator Paterson said the party was taking the findings of the commission seriously and would support any sensible changes to prevent it from happening again.

The report into the scheme included a sealed section that recommended further investigation and action against several unnamed individuals.

Federal police and the National Anti-Corruption Commission are considering the evidence.

The commission declined to say how many people had been referred to it, but confirmed on Monday the referrals would be “assessed in accordance with the commission’s procedures”.

Mr Shorten said he understood the undisclosed chapter would be made public once investigations were completed.

– with AAP