This comes as high-risk close contacts of monkeypox cases in the UK are being urged to self-isolate for 21 days.
The Chair of the HSE's Monkeypox Incident Management Team said it is possible that cases of Monkeypox will be seen in Ireland.
An incident management team has been created so the country is fully prepared for the disease.
The UK Government has ordered Brits who have come into contact with Monkeypox to self isolate for three weeks as more cases are confirmed.
UKHSA confirmed 20 cases in the UK so far - however, the number is expected to rise.
Cases normally occur in Africa, but the disease is spreading to Europe without any links.
Dr Derval Igoe, Interim Director of the Health Protection Surveillance Centre said that people are also presenting without the classic symptoms.
Monkeypox is a viral disease that normally causes flu-like symptoms and a rash that eventually crusts over and heals.
Speaking on RTÉ's Morning Ireland, Dr Igoe explained that there are no link to previous cases.
And it's not necessarily the classical symptoms of Monkeypox.
"And so that's what has been looked at in real detail now and surveillance is underway in all countries in the world" she explained.
Cases spread through close skin-to-skin contact or through droplets when someone is symptomatic.
Dr Igoe said it is important for anyone with symptoms to isolate and for their contacts to be identified.
Anyone with concerns should contact their GP or sexual health clinic.
Many expert groups are working on the best ways to monitor the disease and spread awareness.
"We have our sexual health and infectious disease experts in the hospitals.
"Also our national isolation unit, the virus reference lab, national immunization office and the Department of Health.
"We are also working with Gay Heath Network to make sure the messages are delivered in a suitable way to the populations we know are seeing cases of this virus."