And the Blues' general manager of football Brad Lloyd says his job also could be in danger amid a faltering season.
Lloyd, asked if he and Voss would be at the club next year, replied: "I'm unsure of that.
"We will just stick at it and keep going to work," he told reporters at Melbourne airport on Friday.
"It's for others to judge.
"We have been going at it for a little while now and we have had some good times and some down times like we are now."
Voss is contracted until the end of next season but the Blues' incoming chief executive, Graham Wright, is a renowned agent of change.
Wright will take over from Brian Cook at the end of a season when Carlton appear set to miss the finals.
Voss called for unity after Thursday night's horror 50-point away loss to Port Adelaide, when the Blues kicked a solitary goal in the first half.
But the club's base was tagged overnight with graffiti to "sack the board".
A message "keep Voss" was spray-painted next to a demand to remove Lloyd and head of list management Nick Austin.
"There's behaviours that can work towards getting better outcomes for the club and there are probably toxic behaviours as well that don't help anyone," Lloyd said.
Carlton hold 11th spot with six victories and nine losses. By Sunday night, they could be three wins outside the top eight.
After the heavy loss to Port, Voss said the character of his club would be exposed.
"Now, the answer starts to become about what we value," Voss said.
"What you do find out a lot about is your character - your football team, football club, right now.
"And what connection is needed to be able to ensure that we do get that turnaround.
"There is a way we need to be as a football club - and we're not that yet.
"There has been a lot of foundations laid on that, but clearly that hasn't fully turned to the standard that we want nor the results that we want."
Voss said there must be "collective accountability" for Carlton's failings.
"There is no separating groups here," he said.
"This is collective accountability. We'll look at it thoroughly and see where we need to correct."
The loss to Port followed an upset 11-point defeat to lowly North Melbourne last weekend.
"The way through this - I said this last week - it's not to isolate, it's coming together," Voss said.
"If there's one thing I know about working through really tough times, it's how we connect.
"What we won't do, what you will not see us do, is pass blame on anyone.
"We'll sit here and we'll say, 'What's my role in this?' We'll get to work hard on that but we need everyone on board.
"What I feel right now as a leader is, I feel really disappointed for our people.
"We feel like we're creating a great environment but we're not getting the results we're after.
"We're enormously disappointed ... but it's time to come together, not isolate."
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