The airport said it had begun a consultation with staff on cost-cutting measures, including voluntary redundancy.
It was closed for nearly three months from March 25 due to the coronavirus pandemic.
Chief executive Robert Sinclair said: "It is with huge regret that we are announcing this restructuring programme today and our thoughts are with all of our highly valued staff and their families.
"The aviation sector is in the throes of the biggest downturn it has ever experienced as a result of the pandemic.
"We have held off looking at job losses for as long as possible, but sadly we are not immune from the devastating impact of this virus."
Flights from the site resumed on 21 June but remain well below 2019 levels and this is expected to continue during the coming winter season, the airport said.
It has already cut all non-essential spending and last month announced a "temporary pause" to its £500m development programme, including a new terminal extension.
Aviation has been one of the hardest hit sectors in the coronavirus jobs crisis, accounting for one in four of all publicly-announced cuts recorded in a Sky News tracker.
Gatwick has announced job losses totalling more than 1,300 while Sky News revealed earlier this month that Heathrow could cut 1,200 roles after talks with trade unions about pay and working conditions failed to land an agreement.
Flights were brought almost to a standstill earlier this year and since reopening the industry struggled to return to normal levels, with much of the suppressed demand blamed on changing quarantine rules.
Last week, industry body Airlines UK wrote to the prime minister warning of "economic ruin" unless the government adopts airport testing as a "safe and effective" alternative to quarantine.