Minister for Health James Reilly has said a third tier medical card is one of a number of options being considered.
The minister said he will be meeting the Health Service Executive today to explore options to help people who are in difficulty and suffering hardship.
A final meeting will be held next week to iron out any problems.
Mr Reilly said he has known for some time that there is a lot of concern around hard cases and the processing of information.
He said TDs have been asked to give a list of names of people they believe should have been given a medical card.
He also wants a list of people who have given information to the Primary Care Reimbursement Service only to find that the information has been misplaced.
The medical card issue was discussed at the Fine Gael Parliamentary Party meeting last night.
Fianna Fáil health spokesperson Billy Kelleher has said the number of discretionary medical cards has been reduced by over 30,000 in the last three years.
Figures provided to him in a parliamentary question show that there were 49,596 discretionary medical cards at the start of April.
Mr Kelleher said that last year's HSE Service Plan targeted a reduction in discretionary medical cards.
He said these cards were essential for people with serious illnesses, as the treatment can cause major financial hardship.
The latest figures show that there were nearly 1.8 million medical cards issued, of which 49,596 are discretionary.
There are also 120,981 GP visit cards, of which 29,080 are discretionary.