The California-based brokerage has held talks in the past week with underwriters about moving forward with a filing within weeks, Bloomberg said.
Robinhood did not immediately respond to a request for comment.
Reuters reported last year that Robinhood has picked Goldman Sachs Group Inc to lead preparations for an initial public offering which could value it at more than $20 billion.
Robinhood was at the heart of a mania that gripped retail investors in late January following calls on Reddit thread WallStreetBets to trade certain stocks that were being heavily shorted by hedge funds.
The online brokerage tapped around $3.4 billion in funding after its finances were strained due to the massive trading in shares of companies such as GameStop Corp.