Ferrari say they are "looking around" at their driver options beyond 2017 and want Sebastian Vettel to be "more calm" next season.
The four-time world champion's contract with Ferrari runs out at the end of next season and the German endured a difficult, winless season this year.
President Sergio Marchionne said: "With Vettel it doesn't make sense to talk about renewal now.
"We must first understand if he feels comfortable with us in 2017."
He added: "We must give him a winning car, otherwise talking about the future is useless.
"We know Vettel wants to win with us. Can we guarantee it? In return, he must drive with composure, be more calm, less agitated."
Marchionne's remarks are a reference to Vettel's tendency last year to become audibly flustered on the radio during race weekends - and especially at the Mexican Grand Prix, when his anger at the driving of Red Bull's Max Verstappen led him to launch an expletive-laden tirade directed at race director Charlie Whiting.
The contract of Vettel's team-mate Kimi Raikkonen also comes up for renewal next season. The Finn ended 2016 strongly after a difficult start and out-qualified Vettel 11-10 over the year.
Vettel's 2016 rants
Marchionne said: "We have two world champions and it's up to us to give both a winning car. Then we'll see what happens after 2017."
He said the decision of what to do after 2017 was a "work in progress. I admit we are looking around us.
"I'm happy with Raikkonen's season - he will race again in 2017, but what about after that? Does he want to retire or carry on?"
It is the second time in less than three months that a senior Ferrari figure has appeared to criticise Vettel's attitude.
He added that Vettel "just needs to focus on the car. He is a person who gives so much, and sometimes this means he is interested in a bit of everything - so sometimes you have to re-focus him, remind him to be focused on the main job."
If they chose not to renew the 29-year-old's contract, Ferrari would have difficulty finding a driver of similar status.
Mercedes' Lewis Hamilton and Red Bull drivers Verstappen and Daniel Ricciardo are all under contract until at least the end of 2018 - a year longer in the Dutchman's case.
The only other driver in the superstar category is McLaren's Fernando Alonso, who left Ferrari in 2014 two years before the end of his contract because he lost faith they would ever be able to provide him with a title-winning car.