The SFO had been investigating deals between British Aerospace Engineering and the Saudi government in which BAE was alleged to have paid millions of dollars to Saudi officials.
The investigation was dropped after Saudi Arabia threatened to stop sharing intelligence with Britain.
Earlier this month two high court judges described the government's dropping of the investigation as 'abject surrender' to Saudi threats.
A House of Lord's ruling will decide whether the judiciary is permitted to intervene in such a case.
In an earlier ruling on April 10, the high court had ruled in favour of anti-bribery campaigners fighting to reopen the investigation into BAE, Europe's biggest defence company.
Critics have attacked Tony Blair, Britain's former prime minister, for saying it was right to halt the investigation, which he said would have damaged Britain's national security if it went ahead.
In the earlier ruling high court judges said the fraud authorities and the government had caved in to threats made by Saudi Prince Bandar bin Sultan, the former ambassador to the US and now head of Saudi Arabia's National Security Council, that Saudi Arabia would drop a multibillion pound contract for Typhoon Eurofighter jets.
A $40bn deal for 72 Typhoons was signed in September.
The House of Lord's appeal is now expected to be heard towards the end of this year though no date has yet been fixed.