SFO said that Caterham F1, a now-defunct Formula 1 racing team that was formerly co-owned by Fernandes, was sponsored improperly in 2012 by Airbus' then-parent EADS.
Fernandes denied the allegations and said that the team was part of AirAsia's branding campaign.
In a highly regulated industry where its main rival is state-owned Malaysia Airlines, AirAsia relies on government approvals to support its growth plans and has sought to win favour with the government.
In 2018, days after Mahathir ousted then prime minister Najib Razak in a shock election result, Fernandes apologised for endorsing Najib.
Malaysian authorities have also said they are launching their own investigations into the SFO's allegations.
The allegations come as the Malaysian government evaluates five strategic investment proposals, among them one from AirAsia, to partner with the ailing national carrier, Malaysia Airlines.
Prime-minister-in-waiting Anwar Ibrahim said AirAsia would have to resolve the corruption case if the airline wanted to continue contending for a partnership.
"You can't expect us to consider an entity, when allegations are still there. They have to clear that first to be fair, otherwise we'll be seen to be complicit," he told Reuters in an interview on Thursday.
This story has been published from a wire agency feed without modifications to the text. Only the headline has been changed.
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