The Sydney Morning Herald described Langer's reaction as a "meltdown".
The CA board is reportedly uncertain over Langer's reappointment.
"Justin is contracted as Head Coach through to the middle of this year and we have consistently maintained discussions around the future of the role would commence following the conclusion of the men's Ashes Series," a CA spokesman said.
"We have no comment about those confidential discussions."
Langer took over from Darren Lehmann as Australia's head coach in 2018 following the Cape Town ball-tampering saga.
In 2019, he and newly-elected Test captain Tim Paine helped Australia retain the Ashes in England for the first time in 18 years.
But after losing the Border-Gavaskar Trophy on home soil twice in three years, reports emerged that Langer's intensity was wearing thin with the players.
Leaks emerged from the dressing room about their unhappiness with his coaching style and the cracks remained during horror white-ball tours of the West Indies and Bangladesh last year.
A crisis meeting between CA chiefs and senior players was needed to address the issues between players and coach, sparking suggestions Langer was in danger of not having his contract renewed.
The former Australian Test opener has since taken a step back and delegated more responsibility to his support staff, which has seemingly helped improve the team's performance.
Over the past couple of months, Australia has claimed its maiden T20 World Cup title and comprehensively won a home Ashes series 4-0.
However, Australian Test captain Pat Cummins failed to publicly endorse Langer as coach after retaining the urn.
"I think we'll sit down all together after this series, or whenever his tenure is up and his contract is up for renewal, in a few months we'll visit that then," Cummins said when asked about Langer's position.
"(Langer) has been great. He's certainly still head coach, but I think the environment that he creates not only for the players, but the coaches around him, really empowers them.
"You've seen (batting coach) Michael Di Venuto really take charge of the batting, (assistant coach) Andrew McDonald take charge of the bowling. It's just really good, clear roles for everyone in the team.
"It's in some ways taking a step back and letting the players really dictate the environment they want.
"It worked incredibly well over in the World Cup, and he has huge credit to do with that, and hopefully it continues for this summer. He's been great so far."