Australia Test captain Pat Cummins has stopped just shy of backing head coach Justin Langer to continue.
Langer is out of contract later this year and it remains to be seen whether he will be offered an extension.
Despite recently guiding Australia to their first T20 World Cup win and a dominant 4-0 victory in the Ashes, Langer's coaching style has been a point of contention.
The Sydney Morning Herald claim his 'intense and inconsistent micromanagement style' has created a rift with some players and Cricket Australia may decide against renewing his deal.
The board are set to meet on Friday to discuss a number of key issues, including Langer's future, and both Cummins and white-ball captain Aaron Finch have spoken to their hierarchy about the coach.
When asked on Thursday if he wanted to see Langer remain in charge, Cummins said he has "really loved" working with him but stopped short of calling for Cricket Australia to extend his contract.
"It's part of speculation which I don't think is really healthy," he said. "I just don't want to add to it. That's Cricket Australia's job. It's not my job.
"I've really loved my time working with JL and we've had an evaluation process. I've been part of that, a lot of other players and staff have been part of that.
"Just like when we get evaluated. I've got huge respect for JL, really like working with him. But it's not my call."
Speaking to SEN Radio in January, Langer insisted he did not feel "edgy" about his future.
He said: "No never edgy, whatever happens. Before the World Cup and before these Ashes, we've never ever been better prepared. It's not a coincidence we've had the success we've had.
"Whatever happens from now we can all be incredibly proud of this little period.
"We had two missions to win the World Cup and to win the Ashes, to do that in such a short period is a monumental effort and we're all really satisfied with that, we're all really happy with that, we're all really proud of that.
"I sit here at the moment feeling really content with the last two series."
