Raikkonen currently drives for Lotus and sits second in the championship standings—38 points behind leader Sebastian Vettel—following the Hungarian Grand Prix.
He has been linked with a summer switch to Red Bull, but Bild's Nicola Pohl and Helmut Uhl say Ferrari "has made the Finn an offer."
Where should Raikkonen drive next season?
Red Bull is hoping to partner Raikkonen with Vettel when Mark Webber retires at the end of the season, but it is reported that Ferrari approached Lotus on the Thursday prior to the Hungarian GP.
In the end it could come down to money, with Bild seeing the Ferrari offer as “more lucrative” than that being planned by Red Bull.
Raikkonen also won his only championship title with Ferrari back in 2007, later replaced by Fernando Alonso when he left the Italian outfit in 2009.
Reigning champion Vettel has already made clear who he would like to partner at Red Bull next season, telling the BBC in quotes reported by Ian Parkes in the Daily Mail that he would prefer Raikkonen to Alonso.
I’d prefer Kimi. I need to be careful now, but nothing against Fernando. I really respect him a lot as a driver.
But I respect Kimi on track, off track, because he has always been very straight with me. From that point of view it would be a bit easier.
Credibility has already been given to the potential Alonso switch to Red Bull after team principal Christian Horner refused to deny the Spaniard is in the running for the vacant seat, as reported by Pete Gill of Sky Sports.
Alonso’s cheeky reply that he would like a faster car for his birthday added to the rumour, earning him a public scolding from Ferrari president Luca di Montezemolo.