Two reports, published in November, criticised the regulator at the time for failing to take action.
One of those reports, by barrister Andrew Green QC, said regulators should consider banning 10 former HBOS executives.
A new investigation has now been announced by regulators.
"The Financial Conduct Authority (FCA) and the Prudential Regulation Authority (PRA) have decided to start investigations into certain former HBOS senior managers," the regulators said.
"These investigations will determine whether or not any prohibition proceedings should be commenced against them. The FCA and PRA continue to review materials with a view to making further decisions regarding other former HBOS senior managers."
No details are being given as to the exact nature of the investigations, who is being investigated, or the timeframe of the inquiry.
A Bank of England/FCA report examined the failure of HBOS, while Mr Green examined decisions taken by the Financial Services Authority, the City regulator at the time of the HBOS demise. Both were published in November.
So far the only person to have been banned is Peter Cummings, who was previously the head of corporate lending at HBOS. In 2012, he was fined Â£500,000, and banned from senior positions in banking.
In his report, Mr Green suggested that the Bank of England's PRA and the FCA should consider prohibition proceedings against former executives.
That included Andy Hornby, HBOS chief executive from 2006 to 2009. Mr Green said the FSA was "misguided" when it took the decision not to take action against Mr Hornby.
Other former HBOS executives named in the report included Lord Stevenson, and Mike Ellis, the former group finance director at HBOS.
Lindsay Mackay, the head of HBOS's Treasury division from 2004, could also be banned, November's report said.
James Crosby, HBOS chief executive from 2001 to 2006, has retired. He gave up his knighthood in 2009, and surrendered part of his pension.
Eight former non-executive directors of HBOS were criticised in the report, although they said they disagreed with its findings.
The eight, including Lord Stevenson and Carphone Warehouse founder Sir Charles Dunstone, said the report had downplayed the "unforeseeable" effects of the financial crisis.

The snap drill in the Rostov region was ordered by President Vladimir Putin.
The southern military district includes Crimea - the peninsula annexed by Russian forces in 2014 - and areas on the border with eastern Ukraine.
Pro-Russian rebels also held military drills in eastern Ukraine last week.
The self-styled "Donetsk People's Republic" tested heavy artillery and rocket systems in the Torez area, near the rebel-held city of Donetsk.
Nato, Western leaders and the Ukrainian government accuse Russia of sending heavy armour and regular troops to the rebels. Moscow denies that, but admits that Russian "volunteers" are helping the rebels.
A shaky ceasefire is in place, but both sides - the rebels and Ukrainian government forces - are still far off fulfilling the Minsk peace deal they signed up to.
The Russian military did not indicate any connection between the current exercises in southern Russia and the Ukraine situation.
The exercises include the rapid deployment of troops from 3,000km (1,860 miles) away and the preparation of emergency runways for the air force.
The Organization for Security and Co-operation in Europe (OSCE) said its monitors in the eastern Ukraine conflict zone had seen continuing use of "proscribed weapons, heavy artillery", despite the Minsk agreement.
In a statement to the BBC, the OSCE said the tension levels "still ebb and flow". In late January there were more than 1,000 ceasefire violations "in different places along the contact line", but in early February the conflict zone "remained relatively calm", the OSCE said.
The main hotspots remain: the area north of Horlivka, especially Zaitseve village (about 45km north of Donetsk), also around the Donetsk airport, Debaltseve and the triangle Kominternove-Pavlopil-Oktiabr south of Donetsk.
Russia's exercises come as its air force contingent in Syria carries out heavy bombing to push anti-government rebels away from the city of Aleppo.
Some of Russia's latest military equipment is involved in the Syria mission, including four Sukhoi Su-35S fighters - a type that only entered service with the Russian military last year.
Regulators are to begin investigations into senior managers at HBOS, the bank which collapsed during the financial crisis.
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Russia is holding combat readiness exercises involving 8,500 troops, with dozens of ships and aircraft, in a southern region near areas of eastern Ukraine held by pro-Russian rebels.