The Omanis are understood to want to replace their fleet of ageing Jaguars with one of the most sophisticated fighter jets.
The deal, said to be imminent, could not come at a better time for the Government, which is seeking a way out of buying a further tranche of Typhoons.
Britain is committed to buying 88 Typhoons and is under pressure from Spain, Germany and Italy not to renege on the deal. Cancellation would result in huge financial penalties, but buying 24 fewer would mitigate the cost substantially.
It would also be good news for BAE Systems, which is battling to keep its factories working as the Government considers further defence cutbacks. An order of this size inevitably leads to billions of pounds of maintenance and support work.
A ferocious battle is raging in the Ministry of Defence, as the Royal Navy and Royal Air Force battle to maintain hard-won orders.
At stake are huge contracts for two aircraft carriers, billions of pounds of fighter planes, transport aircraft and armoured vehicles.
BAE and the MoD declined to comment on the negotiations.
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