The two banks had previously been identified as the frontrunners for the deal.
The source confirms that the two banks have now been appointed, although neither Aramco or Dow has officially announced the award of a mandate.
It is understood that the project sponsors were impressed by the track record of RBS and the model it developed on a number of Qatari projects, including Ras Laffan C.
RBS has used a model of approaching a much wider mandated lead arranger group than usual and selling smaller stakes on a take-and-hold basis.
RBS and Riyad Bank had been shortlisted along with HSBC with SABB, from a group of six banks that originally bid for the mandate (MEED 18:5:08).