Those banks have pitched valuations for the company ranging from about $18 billion to $30 billion, the people said.
Uber came under fire more than a year ago after public scrutiny into the company's workplace culture that many said included sexual harassment and discrimination.
Lyft's confidential filing means the Securities and Exchange Commission can review the material and provide feedback before the company publicly files its S-1, which will likely include detailed financial information, risk factors and other material information for prospective investors.
The company was valued at $15.1bn (£11.8bn) at its latest funding round in June, when investors led by Fidelity Investments poured $600m into the firm.
The company was set up in 2012 by technology entrepreneurs John Zimmer and Logan Green, three years after Travis Kalanick co-founded Uber.
The number of shares on offer and the price range for the proposed offering have not yet been determined, Lyft said. The race between them is one of the most closely watched in Silicon Valley. Uber has already disclosed it will go public next year, but hasn't indicated when.
The SEC filing escalates the company's rivalry with Uber, which has been struggling with scandals. They have also invested in rival electric scooter services.
"Lyft has built a very USA -based rideshare business that has done well", Green said.
Getting a head start with its IPO will allow give Lyft a "first-mover advantage" over Uber and help steer investor expectations about the growth and moneymaking potential of ride-hailing services, said Rohit Kulkarni, managing director of SharesPost, which focuses on privately held companies going public.
Both Uber and Lyft have lost huge sums of money by spending heavily competing with each other for passengers and drivers and entering new markets, although they have recently raised prices and reduced subsidies.
Jeff Zell, an analyst at advisory firm IPO Boutique in Florida, said: "With autonomous cars on the horizon, it is anyone's guess where this sector goes in the future". Its investors include General Motors Corp, which holds a 9 per cent stake in Lyft that it acquired for $500 million in 2016, but GM has wound down its co-operation with Lyft, choosing instead to acquire the autonomous auto company Cruise.
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