According to the New York Times, the SEC's probe found that Avellino & Bienes kept "almost no records".
One of its partners, Frank Avellino, told investigators that the $441 million it controlled was actually managed by Mr Madoff.
The newspaper said the lack of records and the fact that Avellino & Bienes promised returns on money it did not control should have raised "red flags".
However, the probe "petered out" with SEC officials apparently accepting Mr Avellino's explanations at face value. Mr Madoff was never questioned in connection with the case.
Speaking to the Wall Street Journal in December 1992, SEC administration Martin Kuperberg said: "There's nothing to indicate fraud."
Mr Avellino's lawyer declined to comment on his relationship with Mr Madoff.
The SEC had previously said it is investigating apparent failures to follow up on "credible and specific allegations" about Mr Madoff dating back to 1999.