"Discussions are now at an advanced stage, [but] any binding agreement to proceed with a merger will still be subject to a number of conditions, including shareholder and regulatory approvals," Alawwal said in a statement.
RBS is part of a consortium, including Santander and Fortis, that owns 40% in Alawwal following the takeover of ABN Amro Bank NV in 2007.
RBS owns just over a third of a stake in the consortium but has to hold £5.9bn on its balance sheet to cover Alawwal if it went insolvent.
Proposed merger to boost RBS balance sheet
The bank has been trying for years to sell down its holding in Alawwal as it shifts its focus to its core UK business.
A merger between SABB and Alawwal would allow RBS to wind down its holding in the Saudi Arabian bank and would cut risk-weighted assets on its balance sheet.
RBS would own 5% in the enlarged group, meaning it would only have to hold just under £1bn on its balance sheet to cover risks.
This could help pave the way for the government to sell down its stake in RBS.
Government could be closer to selling down RBS stake
RBS remains 70% owned by the government following a taxpayer bailout during the 2008-09 financial crisis.
Chancellor Philip Hammond has suggested he is waiting for the bank to resume dividends and for its share price to rise before selling the government’s shares.
Legacy issues have weighed on the bank’s share price and earnings, holding back RBS from resuming dividends.
But in May RBS came closer to resolving its legacy issues by agreeing a US$4.9bn settlement with the US Department of Justice to end an investigation into the sale of mortgage-backed securities.
READ: Investors in RBS breathe sigh of relief as lender agrees smaller than expected settlement with the US DoJ
The penalty was much less than estimates published in the media ranging up to US$13bn and drew a line under an issue that has been hanging over the bank’s head for some time.
The company has also made progress in its turnaround plan, reporting its first annual profit in a decade in February.