The Finn is out of contract at the end of the year, although Ferrari have a further option on his services, but has indicated he wants to stay on alongside Sebastian Vettel.
Team principal Maurizio Arrivabene, who has been complimentary towards the 35-year-old, said he had made the situation clear.
"You want to know what I said to Kimi? He was telling me about the contract and I said to him 'it depends on your performance'," he told reporters at the Bahrain Grand Prix.
"And Kimi, he’s the kind of person that appreciates when you’re talking with him in a very transparent way and straight to his face. Kimi knows, now it’s early to talk about this at the moment.
"I’m happy about the performance of Kimi but he needs to push and he knows that," added the Italian, whose team have made a big step forward this year and are now the closest challengers to champions Mercedes.
Four-times champion Vettel joined from Red Bull at the end of last year and won the second grand prix of the season in Malaysia while Raikkonen has yet to stand on the podium in three races.
However, the Finn has been far more competitive than in 2014 and was quicker than Vettel in both Friday practice sessions in Bahrain.
There has also been speculation about world champion Lewis Hamilton's future at Mercedes, with the 30-year-old Briton out of contract at the end of the year and yet to sign a new deal -- although that is said to be a formality.
Formula One supremo Bernie Ecclestone, perhaps mischievously, stirred the pot when he suggested Hamilton would be a perfect fit for Ferrari.
"It would be great to see Lewis at Ferrari," the 84-year-old told reporters at the Sakhir circuit.
"Whether Sebastian would want that, I really don’t know. But if Lewis went there, it would be great for the sport -- 100 percent.".
(Editing by Ed Osmond)
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