Tánaiste Leo Varadkar told a meeting of the Fine Gael parliamentary party on Wednesday evening that the Government must have a plan in place by the end of May for the phased return of international travel.
Sources told The Irish Times that Mr Varadkar said the aviation sector and airports need a plan in place by then.
It is understood Mr Varadkar also said he wants to see a trial of an outdoor event such as a Leinster match similar to a recent experiment in Barcelona.
Researchers in Spain found “no sign” of higher levels of infection among people who took part in a large test concert last month in Barcelona. Six people tested positive within 14 days of attending the gig but the incidence was lower than that seen in the general population.
Mr Varadkar has also rowed in behind comments made earlier by Green Party leader Eamon Ryan that the main distinction in hospitality should be between indoor and outdoor, as opposed to between outlets that serve food or not.
Mr Ryan also suggested the Government is likely to scrap the requirement for pubs to provide a “substantial meal” while serving alcohol.
Eamon Ryan said he does not believe there will be a distinction between wet pubs and pubs that serve food when hospitality reopens this summer and that it is unlikely it will be based on “whether or not you’re having chicken nuggets”.
The Green Party leader also confirmed the lifting of the inter-county travel ban will coincide with the reopening of hotels to allow people to travel domestically.
Mr Ryan said the “opening up of hospitality is inter-county travel”, adding “the two go together”.
His comments came ahead of a Cabinet sub-committee on Covid-19 meeting on Wednesday to consider what restrictions can be eased next month.
It is expected that next month will see the full return of construction, the reopening of personal services such as hairdressers and barbers, as well as the phased return of non-essential retail.
The resumption of religious services and the reopening of museums, galleries and libraries is also expected next month.
It is anticipated that the Government will also set out plans for June and July when ministers make a decision at Cabinet on Thursday.