Sources close to the Financial Conduct Authority (FCA) said new evidence would be required to trigger such a move.
One of the men, former HBOS chief executive Sir James Crosby, resigned from his role with a private equity firm in the wake of the damning report into the collapse by the Parliamentary Commission on Banking Standards.
But Sir James remains a senior independent director for Compass, one of the country's largest catering firms, as well as a trustee for Cancer Research UK.
Andy Hornby, another of those criticised by the group of MPs and peers, received public support from his employer, Gala Coral, which said he had its "complete backing".
The FCA is preparing a report into how regulators dealt with HBOS, which was bailed out to the tune £20 billion at the height of the 2008 financial crisis.
Sources close to the organisation said its predecessor, the Financial Services Authority (FSA), had already investigated what went wrong at HBOS.
That led to Scots-born former director Peter Cummings being fined £500,000 and banned for life from working in the City. But the commission said it was wrong that Mr Cummings alone should shoulder the blame. In its report the Commission called on the City regulator to also consider barring Sir James, Mr Hornby and the bank's former chairman Lord Stevenson from working in the financial sector.
The commission said: "The primary responsibility for the downfall of HBOS should rest with Sir James Crosby, architect of the strategy that set the course for disaster, with Andy Hornby, who proved unable or unwilling to change course, and Lord Stevenson, who presided over the bank's board from its birth to its death."
A source said it was "not impossible" that there could be a new investigation, to look again at the roles played by other senior executives, but added "there would need to be new evidence for that".
Sir James, who was chief executive of HBOS from 2001 to 2006, was also a former deputy chairman of the FSA. Last night questions remained over whether Sir James and Lord Stevenson should retain their titles. The Royal Bank of Scotland's disgraced former boss Fred Goodwin was stripped of his knighthood last year.
Andrew Tyrie, the Conservative chairman of the banking commission, said it was not its job to make decisions about titles.
David Cameron has claimed the Coalition's changes to financial regulation mean a situation like the collapse of HBOS could not happen again in the future.
He said: "We've changed the entire regulatory system; we've swept away the failed system that Gordon Brown had put in place. That new regulatory system is now there and is now working and will make sure that these things can't happen again."
SNP Treasury spokesman Stewart Hosie said: "Clearly there are serious lessons which must be learnt from the failures that took place at HBOS, and lessons must also be learnt from how the circumstances which led to the collapse of HBOS were allowed to take shape in the first place."
A spokesman for the Treasury described the failure of HBOS as a "symptom of the financial crisis and the regulatory system in place at that time".