Société Générale is looking to establish its wealth management arm as a major Middle East player that is expected to post annual double-digit growth rates in the next three to five years as it seeks to tap the petrodollar-rich region.

"We are optimistic about the region and expect a double-digit growth rate over the next few years. The Middle East is a top priority for us in our global plans," Eric Lorentz, SG Private Banking's new managing director and global market manager for the Middle East, told Zawya Dow Jones on Monday.