The French bank said yesterday that Thiam would be nominated as an independent director at its annual shareholder meeting on May 25.
Some Pru shareholders suggested Thiam had a big enough job leading Prudential through its deal to acquire AIA and launch its £14bn rights issue.
Speaking to the Telegraph, Royal London criticised Thiam, claiming he “ought to be busy with his day job”.
But this afternoon Thiam insisted he would not take up the offer.
He says: “I am very flattered to have been selected for the role of independent director at Société Générale, which is an outstanding organisation.
“But my absolute priority is to continue to focus on delivering strong results for our shareholders and on ensuring the success of the transformational transaction and the subsequent integration with AIA.
“I will therefore not be pursuing this opportunity with Société Générale.”
Thiam become group chief executive of the insurance giant on October 1 last year.