An investigation will be launched into Greensill Capital, the financial firm for which David Cameron lobbied ministers, Downing Street sources have told the Press Association.
No details of the probe into the company, which collapsed into administration in March, have been released yet.
The former prime minister has accepted he should have communicated with the Government "through only the most formal of channels" rather than text messages to chancellor Rishi Sunak as he acknowledged mis-steps over the controversy.
Breaking his weeks of silence, the former Conservative prime minister said in a statement that having "reflected on this at length" he accepts there are "important lessons to be learnt".
The Sun reported that ministers and special advisers across Whitehall have been ordered to declare any contacts with Mr Cameron.
What Gordon Brown said
Mr Cameron's predecessor Gordon Brown called for tougher rules to prevent former prime ministers lobbying within Government, claiming it "brings public service into disrepute".
Former Labour leader Mr Brown said that former prime ministers should not be "lobbying for commercial purposes" and suggested legislation banning the practice for five years if existing rules cannot be made to work.
"I can't comment on the individual detail of this but for me there are principles about public service - it cannot ever become a platform for private gain," the former prime minister told BBC Radio 4's Today programme.
"Ministers must never be lobbying, former ministers, prime ministers, must never be lobbying for commercial purposes. Current ministers should not be entertaining such lobbying.
"If we can't succeed in achieving this stopping by the sort of flexibility of the rules, we are going to have to pass laws to make sure that at least for, say, five years, no serving or former prime minister or minister is ever lobbying for any commercial purpose within government.
"It simply brings public service into disrepute."
How the row surfaced
The row surfaced when it emerged Mr Cameron privately lobbied ministers, including with texts to Mr Sunak, to win access to an emergency coronavirus loan scheme for his employer, financier Lex Greensill.
It was later reported Mr Cameron had arranged a "private drink" between Health Secretary Matt Hancock and Mr Greensill to discuss a payment scheme later rolled out in the NHS.
What David Cameron said
The former prime minister - who was in Downing Street from 2010 to 2016 - said in a statement: "In my representations to Government, I was breaking no codes of conduct and no government rules."
He said that "ultimately" the outcome of his efforts to get Greensill's proposals included in the Government's Covid Corporate Financing Facility (CCFF) was that "they were not taken up".
"So, I complied with the rules and my interventions did not lead to a change in the Government's approach to the CCFF," he added.
"However, I have reflected on this at length. There are important lessons to be learnt.
"As a former prime minister, I accept that communications with government need to be done through only the most formal of channels, so there can be no room for misinterpretation."
Cameron: ‘Many allegations are not correct’
Questions had been mounting over his efforts to secure access for the finance company, which later collapsed, putting thousands of UK steelmaking jobs at risk because the firm was the main backer for Liberty Steel.
Mr Cameron said that "many of the allegations" made in recent weeks "are not correct" as he challenged what he said is was a "false impression" that Mr Greensill was a key member of his team while in No 10.