But with the Muslim holy month of Ramadan, during which the Arab world pretty much shuts down, beginning in early July, BAE may have to wait until August for a conclusion.
Another factor is the Saudi monarchy's human rights record, which has been criticized by British lawmakers in recent months amid hefty and persistent media coverage of allegations of corruption in Riyadh.
In May, the British newspaper The Guardian published documents released by Britain's court of appeal concerning allegations two Saudi princes were involved with a London company that allegedly facilitated money laundering for Hezbollah in Lebanon, an Iranian-backed movement designated a terrorist organization by the United States.
The two princes, who deny the allegations linking them to a sworn enemy of the Saudi monarchy, had sought to obtain a court ruling of sovereign immunity that would have blocked publication of the documents.
In another case, a prominent member of the Saudi royal family is at the center of a U.S. criminal investigation into whether Barclays, a leading British bank, made improper payments in the kingdom, apparently involving a son of King Abdullah.
The Saudis agreed to buy 72 Typhoons in 2007 with a reputed price tag of $8.6 billion.
BAE was secretive about the price details and admitted in December 2012 the delays in completing negotiations on the so-called Salaam Program were depressing its year-end earnings.
The first 24 were delivered in 2012 and 48 more were supposed to be assembled in Saudi Arabia, which is striving to develop a defense industry of its own.
But Riyadh decided to continue having the Typhoons assembled at BAE's facility in the United Kingdom and to upgrade the last 24 aircraft it ordered with the latest technology.
This altered the pricing process, and made the contract more valuable.
But BAE's expectations the Saudis would sign up to the price changes as well as the general inflation in prices the project had already absorbed were soon dashed.
That came hard on the heels of the October collapse of a proposed $40 billion merger with EADS, the Franco-German builder of the Airbus and Europe's aerospace giant.
British Prime Minister David Cameron, who has aggressively pushed British arms exports, visited Riyadh in November 2012 to press the Saudis to finalize the 2007 Typhoon deal.
There have been reports the kingdom is interested in buying 48- to 72 more Tranche 3 Typhoons, a deal that would be worth $7.3 billion to $11.2 billion.
The Eurofighter consortium comprises BAE, EADS and Finmeccanica of Italy, but BAE takes the lead in marketing in the gulf where Britain was the dominant power until 1972 when it reduced its military presence east of the Suez.
However, the Saudis are committed to buying 84 Boeing F-15S Eagles and dozens of helicopters from Boeing and Sikorsky Aircraft, a division of United Technologies Corp., for $33.4 billion as part of a massive U.S. arms package to counter Iran.
BAE concluded a $4.07 billion contract with the Persian Gulf sultanate of Oman in December to buy 12 Typhoons and eight Hawk advanced jet trainers starting in 2017.
That deal got BAE out of the hole, helping to safeguard some 6,000 jobs in the United Kingdom after the EADS merger plan fell through, largely because of German opposition, that would have sheltered the defense titan from the effects of shrinking defense budgets in the United States and Europe.
Meantime, the negotiations with the Saudis dragged on and BAE's delivery rate of the Typhoons slowed to nearly zero, with only two of the jets reaching in the kingdom in more than a year.
Deliveries are now back on track, raising expectations of a conclusion to the complex pricing problem.
There are plans to establish a maintenance and upgrade facility in Saudi Arabia, but BAE executives have their eyes on the ultimate prize: that the kingdom will double its Typhoon order.