A health expert says it is too soon to bring back non-essential travel between Ireland and Britain.
Right now, people flying between Britain and Ireland are advised to self-isolate upon arrival.
Next week the government is set to look at allowing movement between the two islands without restrictions.
DCU professor of health systems Anthony Staines said there are a large number of Covid cases in Britain linked to the Indian variant.
He says resuming travel while this is the case is not a good idea.
"It seems to be more transmissible than the variant we have here right now which came from the UK before Christmas and we saw what happened then," said Prof Staines.
"It is not clear whether it is more severe but it certainly spreads more. We hope - we don't know - but there is some indication that the vaccines will protect against it but we actually don't know that yet."
He believes that until Britain is able to bring that particular variant under control there is an unnecessary risk in non-essential travel between Britain and Ireland.
Public Health England has revealed four people have died with the Indian variant in the UK.
There are reports UK government scientists want to extend the vaccine rollout - to all adults - in areas that are having problems with the mutation.
The British Prime Minister’s to hold a Downing Street news conference this evening and is expected to discuss efforts to tackle its spread.
Pat Dawson, CEO of the Irish Travel Agents Association, is in favour of the move to restriction-free travel between Britain and Ireland but says people are still cautious about going on holidays.
He said the appetite for travel isn't there yet and this is likely to remain the case until people are fully vaccinated.
However, Ryanair CEO Eddie Wilson said international travel needs to restart quickly and that we need to give a "signpost" to people to say that we are open.