DEFRA said another option being considered for the York-based laboratory was to team it up with other public-sector organisations.
Both options are being assessed as part of the government's wider Civil Service Reform Plan.
Regardless of the outcome due to be concluded in early 2013 a DEFRA spokesman said FERA would continue to provide "world-class scientific services that are essential for government".
He added: "We are looking at how we can help FERA withstand challenges and continue to thrive. This includes considering alternative business approaches, perhaps involving partnership with public or private sector bodies. This is work-in-progress and no decisions have been made."
FERA chief executive Adrian Belton confirmed talks were ongoing about the organisation's future direction.
"We are working with DEFRA, our parent department in government, on business plan options that align with the government's Civil Service Reform Plan agenda. That will better position FERA to take advantage of its unique position as a provider of public and commercial sector research and knowledge-based services in agri-food," he added.