It is over a decade since the last such event took place in the capital, but the idea is now being championed by the sport’s new owners Liberty Media.
New F1 chief Chase Carey recently told the Times newspaper that he is alarmed by the lack of promotion of the Silverstone race.
“You could walk though London and not even know the grand prix was on,” he said.
London’s Westminster City Council confirmed that talks are taking place about a potential “showcase event”.
“Discussions are at a very early stage and as such nothing has been agreed,” said a spokesperson.
If the event does go ahead, it will re-fire speculation that Liberty could be looking to run a world championship race on the streets of London.
“London is a great city, and there is no question when you think (about) where are the cities you want to be in,” Carey recently told the Telegraph.
“We are talking to a lot of people. Realistically I have got a page-long list of places that would like to have races,” he added.