Rail and bus commuters with annual tickets are in line for refunds.
The National Transport Authority (NTA) said it is working on solutions to refund those who have paid for tickets but are not using them due to the lockdown.
Refunds are likely to be issued to annual commuter ticket holders due to the fact these people have paid in advance for travel on train, tram, bus and rail services, but the current travel restrictions mean they are not using the tickets.
Talks between the NTA and the companies it regulates, which include Irish Rail, Bus Éireann and Dublin Bus, are ongoing on the issue.
A spokesperson for the NTA said it was trying to come up with a solution that works for the greatest number of commuters.
"Along with the operators and other stakeholders, we're teasing out the issues, and hope to be in a position to announce something very soon," the spokesperson from the NTA said.
Monthly ticket holders who had paid to travel in either March or April may also get refunds.
Annual and monthly tickets can be bought using gross salary, saving on income tax and USC.
Consumers have been advised to retain any monthly tickets that they have bought in case they are needed to claim a rebate.
Fianna Fáil TD for Dún Laoghaire Cormac Devlin called on the Government to relax the rules surrounding the Taxsaver Commuter Scheme during the ongoing Covid-19 crisis.
Mr Devlin said the Government should "introduce practical solutions like allowing commuters pause their contributions until the Covid-19 crisis passes, or adding two or three free months at the end of this year's contract".
So far, refunds have been announced for those with health insurance, with some gyms suspending payments as they have been forced to close.
Motor insurers are now under pressure from Finance Minister Paschal Donohoe to refund some of the cost of premiums due to lower traffic volumes and a collapse in injury claims.
However, airlines have come under criticism for their failure to pay refunds despite this being a legislative requirement when flights are cancelled.
Consumers are up in arms over Ryanair and Aer Lingus offering them vouchers to use on flights at a later date, instead of refunds that they have requested.
The airlines are insisting that people can still get refunds, despite reports of consumers finding this difficult.