The one-day event might be organized in the week with the British GP.
Formula 1's bosses have contacted Westminster City Council about the possibility of hosting an event in central London this summer, and discussed a possible street demonstration.
Several ideas were put forward, including a run on the British capital's roads, with a focus on making it a family day out.
It is hoped the one-day event could take place in the week leading up to the British Grand Prix, which takes place on July 16.
Although the idea was tabled, putting together a demonstration ahead of the Silverstone race this year will be challenging given the short timescale.
The prospect of a grand prix on the streets of London was not on the agenda.
"Officers from the Greater London Authority and Westminster City Council have met with event organisers about a potential showcase event in central London, not a race," said a Westminster City Council spokesperson.
"Discussions are at a very early stage and as such nothing has been agreed."
Motorsport.com understands that the council is currently compiling a report to provide feedback to F1's bosses on what would be feasible.
If a demonstration run gets the green light, it would be the first of its kind in London since eight F1 teams completed a course between Regent Street and Piccadilly Circus in 2004.
There has long been talk of a potential grand prix on the British capital's streets but none have come close to fruition.
Last month, an amendment to the Road Traffic Act was passed in the UK parliament, simplifying the process for motorsport events in England to incorporate the use of closed roads.
Previously, any event wanting to used closed carriageways had to pass an act of parliament.
With the amendment to the RTA, the decision to grant closed-road permits now lies with the Motor Sports Association - motorsport's governing body in the UK - and the affected local councils.
However, there still remains a series of obstacles that would need to be overcome to enable an F1 race to take place in a city centre.