The company is hoping it will have the final go-ahead from the agency by September.
Special approval will be needed as the A350 will fly on routes over long stretches over water.
The new lightweight, medium-sized jet has been developed to compete with Boeing's Dreamliner.
Airbus already has delivery orders to fulfil, with the first A350 going to Qatar Airways, around the end of the year.
The A350 intercontinental jet will seat between 250 and 350 passengers.
While European regulators may sign off on the jet before the end of summer, the US Federal Aviation Administration may take a few months longer.