But Kobayashi, 27, has also collected millions from his fans to offer to a potential F1 race employer, and just before Christmas was spotted at Caterham's factory.
When asked about the popular former Toyota and Sauber driver, a Caterham spokesman told Sky: "There are lots of drivers being linked with Caterham at the moment which is very good news for us.
"I think it's flattering that somebody of Kamui's experience, talent and popularity would be linked to our team.
"We will be making an announcement on drivers in due course and there are a number of drivers of Kamui's experience who are being considered."
Giedo van der Garde and Charles Pic drove for the team in 2013, but so far neither have been confirmed for the new season.
Along with Kobayashi, rookie Marcus Ericsson and former team driver Heikki Kovalainen have also been strongly linked with the seats.
The Caterham spokesman admitted that "at least one" of the team's 2014 drivers will be experienced.
"It's particularly important with the new rules and the new car configuration that you have somebody who has some experience," he said.
The spokesman added that Caterham is "very, very close" to making an announcement.