The Japanese was sidelined two weeks ago at Spa-Francorchamps, as reigning Le Mans winner Andre Lotterer and his sponsor Hype stepped into the green car.
Caterham's new management intended to run the Russian-backed Spanish rookie Roberto Merhi in Monza, but it emerges that the FIA only granted him permission to drive in Friday practice, given his F1 inexperience.
It is believed the Leafield-based team, headed by Colin Kolles, now fully intends to give the 23-year-old his race debut in Singapore, after the FIA is satisfied with Merhi's practice performance at high-speed Monza and grants him a super license.
Lotterer, who performed strongly at Spa but retired early from the race with a loss of power, has revealed he was offered the race seat for Italy but turned it down.
"When Colin Kolles told me on Tuesday that Merhi would take my place for the first practice session, I changed my mind and told them I would not participate," said the Belgian-raised German and works Audi sports car driver.
"I am a newcomer in formula one and I need to drive," said Lotterer.
Multiple sources are now reporting that Japanese Kobayashi, whose name is already showing above the Caterham garage at Monza, is en route to Italy.
"I am headed to the country of pasta," the 27-year-old wrote in Japanese on Twitter.
Kobayashi reportedly continues to lack adequate sponsorship for the seat, but Caterham has already run three drivers in 2014 and wants to keep the fourth open to Merhi for Singapore and beyond.