Ms Gleeson was driving unaccompanied on a learner permit.
Road safety campaign group PARC insisted the legislation was "a no-brainer".
"When a garda stops a learner driver and charges him or her for driving unaccompanied, it makes no sense whatsoever that the garda must then allow that driver to continue their journey driving unaccompanied," a PARC spokesperson said.
In a Dáil reply, Mr Ross acknowledged that, in terms of learner drivers, the law may need to be changed.
"Currently, gardaí have the power to detain vehicles in a number of circumstances such as where the vehicle is untaxed, uninsured or does not have an NCT," he said.
"An extension of this power to cover vehicles being driven by unaccompanied learners would require an amendment to Section 41 of the Road Traffic Act, 1994.
"I would like to advise that this is something that I am willing to consider in the context of future road traffic legislation."
Tommy Broughan TD had asked whether gardaí currently have the power for such a crackdown on unaccompanied learner drivers.