It is expected testing and tracing Covid-19 cases will cost hundreds of millions of euro by the end of the year.
The HSE has spent around €35m on testing and tracing so far but is expecting that to ramp up.
The head of the HSE Paul Reid says they will also have to start looking at re-opening other parts of the health service that have taken a back seat because of Covid-19.
He says: "We are going to have to have the capacity to do testing and tracing process while at the same time [...] migrating back to non-Covid services
"Unfortunately it can't be an either-or for us, we can't turn the dial down on one. So it is an extra demand on us but we will have to meet the demand while migrating back to a level of safe non-Covid services."
Testing for Covid-19 has expanded to include close contacts of people who have Covid-19 even if they have no symptoms.
It is estimated that around half of people with the virus are asymptomatic.