Three-quarters of the HSE's computer servers have now been unlocked, after last month's cyber attack.
HSE chief executive Paul Reid will tell the health committee the ransomware attack on May 14th severely disabled a number of systems.
He says it led to the complete shutdown of the HSE's computer network.
Mr. Reid says it's taking some time to restore.
But he says 75% of the computer servers, which were locked by the hackers, have now been decrypted.
"We don't know how long it will take to do that final 25%," says Technology Correspondent Jess Kelly.
"It can be a very arduous process if we look at examples from Scotland and elsewhere - other countries around Europe. It could take months."
Mr. Reid says 70% of the HSE's end-user devices, such as laptops, are now available to staff.
"Some appointments have returned. Critically we know that in the east, the large voluntary hospitals - they weren't as impacted as other parts of the country," says HSE's chief operations officer, Anne O'Connor, says outpatient appointments are still badly affected - with only about half going ahead.
"Sites have been gradually returning. We are at about 50% to 60% of our capacity now. General outpatients and critically our radiology outpatients is where we had our biggest problems," she continued.
She says there will continue to be interruptions to services for many more weeks.