Taoiseach Leo Varadkar has confirmed that he wants the country to be "almost fully open" by the middle of next month.
Hairdressers and beauty salons could open sooner than the current planned date of July 20.
However Mr Varadkar warned that there is always a risk that the virus could "make a comeback", which would delay any reopening.
He told RTE 2fm's Breakfast Show that plans will be discussed this week to fast-forward phases four and five of the Government's roadmap.
The Fine Gael leader said that the original plans to enter phase 5 in August were "too slow".
The Taoiseach also went on to say that Ireland has a racism problem and some statues of racist figures may need to be removed.
In recent days, statues of people linked to the slave trade have been taken down around the world.
Asked if Ireland has a racism problem, he added: "I think we do. Every country in the world has racism to some degree.
"Thankfully we do not have the kind of problems with police brutality that we see in the United States, we have a very professional police force and we're grateful for that.
"If you look at the Traveller community and how they are treated and spoke about - that's a form of racism.
"Anyone who grew up in Ireland mixed race like me would be aware of the fact that when you look and sound different - people treat you differently and it is not nice."
Mr Varadkar said as a mixed race person growing up in Ireland, he has experienced racism.
"It is not something I speak about too much but it has not held me back - it has probably pushed me on. I have had a lot of privileges that have helped to counteract that."
"It does worry me that young people of colour who grew up in Ireland are being treated as though they are not fully Irish."
