The Central Bank will today call for more powers to make individuals accountable, after the Davy stockbrokers scandal.
It will tell the Oireachtas finance committee that its existing enforcement powers aren't strong enough.
Davy was fined a record €4.1m last week for wrongful trading practices by 16 of its employees in 2014.
The company yesterday closed its bond desk, as the controversy continues.
Finance committee chairman John McGuinness says the Gardai should be involved in the investigation.
"Every agency of the state should be involved. We have to see now if the Central Bank will take action against the individuals concerned, and if they deem it necessary to send the files to the Gardai, or the Director of Consumer Enforcement.
"It's hugely important that we get to the end of this problem."