Ryanair is calling for all travel restrictions between Ireland, the UK and EU to be lifted by the end of this month.
He says it's "not unreasonable" to ask for clarity on when people can travel freely again.
The EU's digital green certificate system to restart international flights is due to be finalised shortly.
Health Minister Stephen Donnelly yesterday said the EU system could be in place by late June or Early July.
Meanwhile, The Irish Times today reports the Government is also looking at plans to open a 'travel bubble' between Ireland and Britain over the summer.
Currently, all passengers arriving into Ireland - including those from the UK - have to home quarantine, with only a few exceptions.
The stricter hotel quarantine requirement applies to arrivals from 62 'red list' countries.
Ryanair CEO Eddie Wilson told Newstalk Breakfast that his company wants the rules relaxed as soon as possible.
The airline also wants mandatory hotel quarantine rules removed for the EU countries - France, Belgium and Luxembourg - still on Ireland's red list.
Mr Wilson said: “Everyone isn’t travelling necessarily for tourism. You’ve got a lot of people who are discommoded for family reasons, business reasons etc… - you’ve got to give a signpost for people to say we’re open.
“On mandatory hotel quarantine, we’re talking about [lifting] it for the remaining countries in the European Union.
"It was lifted last week for Italy and Austria… but we still have the situation where you can’t travel from France or from Belgium."
He was speaking on the same day Taoiseach Micheál Martin is travelling to England for a meeting with British Prime Minister Boris Johnson.
The Ryanair CEO argued: “We have the Taoiseach travelling to the UK today - presumably he’s not going to do a home quarantine for 10 days when he comes back… I’m sure people can see the inconsistency in that.
“There are people who want to travel today to France and Belgium who cannot do it because of mandatory hotel quarantine."
Mr Wilson was also questioned on whether people who book flights for later in the summer will be able to change their plans if COVID-19 restrictions remain in place.
The airline chief insisted that anyone who books up until the end of June "can change their flight without any penalty" - saying that's been the same with most airlines.