Virtu is seeking to raise as much as $250m at a $3 billion valuation from a listing, people familiar with its thinking have previously told the FT.
Discussions over the role of high-frequency trading in modern markets has intensified in recent days as Michael Lewis, the author of Liar's Poker and The Big Short, released a book taking a closer look at the industry.
Its publication comes just weeks after Eric Schneiderman, the New York Attorney General, revived a long-running and vociferous argument against HFT by targeting the relationship between stock exchanges and trading firms in the latest part of an investigation into he calls "Insider Trading 2.0".
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In its IPO filing, Virtu admitted that it suffered from material weaknesses in its accounting. It also said US regulators at the Commodity Futures Trading Commission are looking into its participation in certain incentive programmed offered by exchanges from July 2011 to November 2013.
In promoting Flash Boys: A Wall Street Revolt, Mr Lewis has repeatedly said in televised interviews beginning with CBS' 60 Minutes that he believes the US stock market is "rigged" in favour of ultra-fast trading firms, among which Virtu has carved an enviable reputation.
The debate intensified on Tuesday after one of the heroes of Mr Lewis' book, Brad Katsuyama, the co-founder of IEX, a trading platform that does not cater to speed traders, appeared on CNBC. Along with Mr Lewis and William O'Brien, the president of Bats Global Market, the three shared a heated discussion over the contents of the book and the evolution US market structure.
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"Shame on both of you for falsely accusing literally thousands of people and possibly scaring millions of investors in an effort to promote a business model," Mr O'Brien said.
To which Mr Katsuyama responded by reiterating that he believed the US market was in fact rigged and that Mr O'Brien was "a part of the rigging".
Last week, Mr Katsuyama said in an interview with the FT that Virtu traded on its platform and that it was "a positive contributor" to IEX.