In 2020, Mr Cameron tried to persuade ministers to allow Greensill - who employed him as an adviser - to join a scheme called the Corporate Covid Financing Facility (CCFF).
This would have allowed the company to issue loans, insured by the government, to help firms through the pandemic.
However, Mr Cameron - and the company's founder, Lex Greensill - were unsuccessful in their attempts.
Greensill Capital collapsed this year, with the loss of 440 jobs, and possible billion-pound losses for investors.
BBC's Panorama has obtained a letter from Greensill Capital to the former PM which suggests that he made £3.29m after selling a tranche of Greensill shares in 2019.
As well as the shares, Mr Cameron is reported to have received a salary of $1m (£720,000) a year as a part-time adviser.
The programme also understands that the former prime minister was paid a bonus of $700,000 (£504,000) in 2019 on top of his salary.
In total, it looks like he made around $10m before tax for two-and-a-half years' part-time work.