Oil industry insiders believe Sir David, with his passion for Europe, will want to take advantage of this unique opportunity. But he may be reluctant to sever ties with the company with which he has been associated for most of his life. BP confirmed yesterday that Sir David had been approached. "He would very much like to be involved in shaping the UK's relationship with its European partners but he is also keen to continue as chairman of BP," the company said.
Sir David will spend the next few days considering the offer and will discuss it with Mr Blair in greater detail.
The possibility of Sir David taking an active role in shaping Labour Government policy on Europe was first mooted in private meetings some months ago but a formal approach was only made on Friday. The precise nature of the appointment and how it would work in practice remains unclear.
The approach is understood to have been made because of Sir David's European credentials rather than his political persuasion. Sir David is well known for his pro-European views and is a great believer in a fully intergrated and properly monitored and regulated single market. He would support European Monetary Union providing the circumstances were right.
He speaks most European languages fluently and his Gallic mannerisms reflect the upbringing by his stepfather, a French wartime fighter pilot who fought alongside Charles de Gaulle.
Sir David has developed important networks of business contacts both in Britain and in Europe. He has served on a number of European committees and working parties where he has earned the respect of his continental partners.
Although Sir David has no direct political experience, he is regarded by colleagues and competitors as an extremely astute political operator.
Industry observers point out that BP is one of the country's most political organisations, and Sir David's experience in rising to the top of that corporation provides the perfect grounding for a political career.
Sir David was appointed as BP's chief executive in 1992 following the contentious departure of his predecessor Bob Horton. He became chairman in July 1995.
Under his command, BP's standing has been transformed. The shares hit a low of 178p a few weeks after Sir David was appointed chief executive but have risen without interruption since, hitting an all-time high of 760p two months ago.