Nugent is under fire in the wake of an explosive review into Australia's worst performance in the Olympic pool in 20 years which has sparked an investigation into allegations of drunkenness, abuse of prescription drugs and bullying.
Nugent this week claimed there were no "overt" problems in his team in the lead up to London, but was contradicted by a number of his swimmers, who said he was aware of disruptive behaviors and had chosen to ignore them.
"I personally don't trust him to be our head coach," Schlanger, who won a freestyle relay gold at the London Games, said in comments published by The Australian newspaper on Saturday.
"His story changes every day. How can he stand up in front of the team and tell us what we can and can't do?
"The situation has become far too volatile for him to remain as head coach.
"If he was a football coach in any code, his job would have been taken away already. The fact that we are an Olympic sport shouldn't make us any different."
Schlanger's comments have underlined the faultlines running through Australia's swim team, which managed a single gold in the relay at London and no individual titles.
Governing body Swimming Australia (SA) has been rocked by admissions from five of the six members of the men's freestyle relay team that they took a prescription drug banned by their national Olympic committee as part of an unofficial "bonding" exercise at a pre-Games camp in England.
The swimmers, who finished a disappointing fourth in London after being favored to win the gold, also admitted to engaging in "childish" pranks which included banging on team mates' hotel room doors late at night and other disruptive behaviors.
Emily Seebohm, who won a backstroke silver at London, told local media this week that she had reported the incidents to Nugent, but her concerns were not taken seriously.
Nugent later conceded he had heard the complaint but failed to act as he did not know the swimmers' identities.
Australian Olympic Committee secretary-general Craig Phillips said Nugent could have handled the incident better.
SA were unable to provide immediate comment when contacted on Saturday, but the governing body's president this week said Nugent still had their full support.
(Reporting by Ian Ransom; Editing by Greg Stutchbury)