Negotiations are still ongoing but sources close to them are confident that the Gulf state will confirm its intent to purchase 12 planes - a contract worth in excess of £1bn.
It is believed the aircraft will be built at BAE's factory in Warton, Lancashire, thereby securing thousands of jobs.
Last month Prime Minister David Cameron visited Jordan, Saudi Arabia and the UAE on a trade mission to promote BAE and persuade the states to buy British-made defence equipment.
It is unusual for a British Prime Minister to promote defence companies so openly but the Government is seeking to build closer ties with friendly Middle Eastern states in the face of what it sees as a growing threat in the region from countries like Iran.
The move also demonstrates an attempt to forge links outside of the traditional Nato countries.
It is thought that Saudi Arabia is eager to add to the fleet of 72 jets already ordered from BAE and the UAE is deciding between BAE and French rival Dassault, maker of the Rafale jet.
If all the contracts were successful, they would be worth more than £6bn collectively - a huge boost for UK plc, BAE and hundreds of smaller companies in the supply chain.
Cuts to defence budgets globally have resulted in a tougher and more competitive market, and BAE had hoped a merger with a company that specialises in civil aviation would lessen any effect of budget cuts.