Mr Harris said he was examining whether his department could introduce additional tax relief for home-based childminders when Budget 2027 is announced on 6 October.
Under the current arrangements, self-employed childminders operating from home can earn up to €15,000 a year without paying income tax on that income.
Mr Harris said the existing relief has not been increased for several years and suggested there was a case for reviewing it.
"I'm looking at if there is a tax relief available in my own department to support people who are child-minding in the home. It hasn't been increased in quite a number of years and I'm positively disposed to that as well," he said.
The potential measure comes as the Government faces continued pressure to make childcare more affordable while also increasing the availability of places.
Mr Harris said childcare would be a key area of focus in the upcoming Budget, as the Coalition works towards its commitment to reduce costs for families.
"Childcare will be, and we've said this right across Government, childcare will be a priority area [in the Budget]," he said.
The Government has previously committed to bringing childcare costs down to €200 a month, while also addressing capacity and access within the sector.
The proposed childminder measure is one of several issues being considered as ministers finalise the details of Budget 2027.
Mr Harris has also indicated that the Government is considering changes to taxation and other supports in response to rising household costs, including measures relating to home heating oil.
