British services company Serco
The Sunday Telegraph reported earlier that the bid had been rebuffed but Serco was sweetening its offer.
Serco said in a statement late on Sunday that it is not in any discussions regarding any major transaction at this time, without elaborating further.
If the deal were to go through, it would make Serco, which manages services for Britain's schools and armed forces and runs prisons and rail services, the biggest foreign company providing services to the U.S. government, the newspaper said.
SRA is a Fairfax, Virginia-based defense consulting firm.
Serco, advised by UBS, was thought to have made its initial offer some weeks ago, the Sunday Telegraph said.
(Writing by Michael Roddy and Karolina Tagaris; Editing by Diane Craft)