But not quite yet.
Sir Simon announced to the orchestra earlier today that he won't seek reappointment when his current contract expires in 2018.
The timing leaves the Berlin Philharmonic plenty of time to find a replacement (and Sir Simon to find a new job, assuming he wants one).
*UPDATE* - Berlin Philharmonic Press Release:
"In 2018 I will have been with the orchestra for 16 years. Before this I was chief conductor in Birmingham for 18 years. In 2018 I will be nearly 64 years old. As a Liverpool boy, it is impossible not to think of the Beatles’ question, “Will you still need me...when I’m 64?” and I am sure that then it will be time for somebody else to take on the magnificent challenge that is the Berliner Philharmoniker."
"This was not an easy decision. I love this orchestra and therefore wanted to tell them my decision as early as possible. I deeply hope that this will give them enough time to start new plans. I look forward with great pleasure to our next five years together and hopefully many years afterwards. I am thankful for the time that we have spent together so far."