Commissioner Nóirín O'Sullivan denied a decision to refer the matter to GSOC was meant to keep it from the public.
It follows the revelation that large sums of EU funding were put in a bank account in a former officer's name.
The parliamentary Public Accounts Committee (PAC) has also been investigating the allegations.
For several months, the PAC has been investigating how accounts at the training college in Templemore, County Tipperary, including one designed to cover laundry bills, were used for other purposes including paying restaurant and entertainment bills.
Commissioner O'Sullivan has, in the past, described what happened at Templemore and the evidence of poor financial controls there as a legacy issue.
The money involved in the GSOC investigation came from an EU-funded training programme, and the commissioner told the PAC the account predates her time and that of her predecessor as commissioner, Martin Callinan.
She said the account operated from Dublin over an 11-year period, from 1999 until it was closed in 2010.
She said her understanding was that this was a police account and that the amounts in it ranged from 5,000 euros (£4,000) to just over 90,000 euros (£79,000).
The recent revelations about Templemore come at a difficult time for Ms O'Sullivan, who has faced several opposition calls to stand down over a number of issues, including her handling of police whistle-blowers and the disclosure that police officers had significantly exaggerated the number of breathalyser tests carried out.
With a new taoiseach (prime minister), Leo Varadkar, and a new justice minister, Charlie Flanagan, there is considerable interest in political circles in Dublin about whether the new office holders will show the same support for Commissioner O'Sullivan that their predecessors and the previous cabinet did.
Ireland's policing watchdog, the Garda Síochána Ombudsman Commission (GSOC), is to investigate alleged financial irregularities at its training college.