The agreement will see SABB - 40 percent owned by the UK's HSBC - acquire Alawwal, which is 40 percent owned by Royal Bank of Scotland - for 18.6 billion riyals ($4.96 billion).
"A binding agreement is yet to be entered into between Alawwal Bank and SABB", they said. "Any binding agreement to proceed with the merger will be subject to a number of conditions, including SAMA [central bank], other regulatory authorities, and the shareholders' approval".
RBS acquired a stake in Alawwal via its ill-fated takeover of Dutch bank ABN Amro in 2007, which played a big part in RBS's near-collapse and subsequent 45.5 billion pound rescue by the British taxpayer in 2008.
The SABB-Alawwal deal, by contrast, is primarily motivated by the desire by RBS to exit the Saudi market, according to Aqib Mehboob, a senior analyst with Saudi Fransi Capital.
The source said it also marked a milestone for RBS, bringing the bank's decade-long effort to rid its balance sheet of trillions of dollars in unwanted assets closer to a conclusion.
Although RBS itself only owned 15 per cent of the Saudi Arabian bank, it held all of the consortium's risk-weighted assets on its balance sheet.
This announcement does not mean that the proposed merger will be agreed between the two parties or that an offer will be eventually made by SABB to Alawwal Bank shareholders in relation to the proposed merger.
The boards of SABB and Alawwal agreed to the takeover on Wednesday in Saudi Arabia's first major banking tie-up for around 20 years.
If everything goes to plan, the process could be completed by the end of 2018, two sources close to the merger said.
Based on the preliminary agreement, Alawwal shareholders would receive 0.485 SABB shares for each Alawwal share, it was announced.
A potential merger would value Alawwal's existing issued ordinary share capital at approximately about 18.6 billion riyals (S$6.7 billion) and a premium of 29 per cent on Monday's closing price.
News of the $5bn deal - which many expected would be priced lower, since RBS was likely to be a keen seller - caused Alawwal's shares to surge the maximum 10 per cent on the open in Riyadh.
The combined entity is valued at a price to book ratio of 1.4 and 14 times price to earnings for the full year of 2018, said Jaap Meijer, managing director and head of equity research at Arqaam Capital in Dubai.