There are calls for a new traffic light travels system for the US and Canada, and for 'formal talks' with the two countries to ensure Irish people can come home for Christmas.
The Oireachtas Transport Committee has recommended people from red-listed EU countries shouldn't have to restrict their movements if they've got a negative COVID-19 test before departure.
As part of its report on the aviation sector, the committee says it wants a strategy developed to allow more international travel in 2021.
It also says the price of a PCR test for passengers should be 'more affordable' and shouldn't be more than €50.
Their recommendations also call for formal talks with the US and Canada to lift an entry ban on Irish citizens, and to have a traffic light system for other countries such as Australia and New Zealand.
Committee chair Kieran O'Donnell says there needs to be a system to facilitate travel from outside the EU.
He said: "We're asking the Government that they would expedite coming up with bilateral agreements with the US and Canada so Irish people can come home at Christmas."
He stressed their recommendations are all focused on "reducing the risk of COVID".
Transport Committee member and Fianna Fáil TD Cathal Crowe, meanwhile, believes the current approach to travel needs to be reviewed.
He said: "The mantra in Ireland by Government and all in aviation at the moment is 'essential travel only'.
"I think that mantra has to change, and the mantra should be you travel safely.
"If you can go for a test and arrive at your departure gate, you can say 'I have been tested, I am COVID-free' and you can board the plane."
He argued that the current approach of only essential travel is 'crippling' the country's tourism sector.
Earlier, the Tánaiste Leo Varadkar said he's hopeful people will be able to go on foreign holidays next summer.