According to the article you referenced, both Saudi Arabia and Iran are looking to formally join the BRICS group of countries as official member states.
The BRICS countries--Brazil, Russia, India, China, and South Africa--is an international political is made up of some of the fastest growing economies in the world and, as per this article from Politics Today, "has been working together [to] challenge the dominance of traditional Western powers." Those being, largely Western European and North American NATO countries.
According to that same article, Saudi Arabia (as well as Argentina) has expressed interest in joining the group. It's hard to say if both Saudi Arabia and Iran will get their bids to join; they certainly both fit the criteria of being fast-growing and largely anti-western in terms of culture. However, as traditional enemies, the Sunni Saudi Arabia and Shia Iran regimes may cause discord in the group if both are to join, perhaps endangering their bid status.
