The Times reports that F1 supremo Bernie Ecclestone will sink £35 million into the plans, which he claims "would be fantastic, good for London, good for England — a lot better than the Olympics".
The proposed 3.2-mile circuit would run past sites including Buckingham Palace, Trafalgar Square and Big Ben, and the paper claims that the race would instantly rival Monaco as the most eye-catching on the calendar.
The 81-year-old Ecclestone is reportedly desperate to make the London race happen, so much so that he will offer to promote it himself - an unheard-of offer at a time when governments across the world are willing to pay £30m for the rights to stage a grand prix.
London Mayor Boris Johnson gave the idea a cautious thumbs up, saying that he was, "always interested in projects that attract jobs and bring growth," and, "am broadly positive providing we can satisfy the air quality and noise issues."
Billionaire Ecclestone - who is currently in the spotlight for all the wrong reasons after a banker he paid £10m to was jailed on bribery charges - claims that the race would pay for itself, attracting 120,000 spectators and generating up to £100 million for the British economy.
London played host to a Formula One demonstration event in 2004 in which cars raced up and down past Piccadilly Circus.
"With the way things are, maybe we would front it and put the money up for it," he told the newspaper.
"If we got the okay and everything was fine, I think we could do that."
Any future grand prix in London would have to be in addition to the British GP, as Silverstone has a long-term deal in place.