Labour have called for the UK to stay in the customs union, but there is no precedent in EU law to grant its demand for a role in trade deals negotiated by Brussels.
However, the Taoiseach appeared to open the door to a potential compromise, saying on arrival at an emergency EU summit to decide on a further delay to Brexit that the UK “could not be a silent partner” if it remained in a customs union.
“Ultimately the European Union, we are the biggest trading bloc in the world. We trade more than China. We’ve a bigger population than the US. And, in a world of big blocs, it’s in the interests of the UK to be part of one of those blocs. It is also in our interests to have the UK in our bloc.
“I think we would be generous negotiating that, understanding that the UK could not be a silent partner in such an arrangement. It would have to have a say in decisions being made.”
Talks between government ministers and Labour front benchers are set to resume on Thursday, with both sides saying they remain committed to the process despite little sign of a breakthrough.
While other EU leaders struck a tougher tone - particularly France's President Emmanuel Macron - Mr Varadkar said EU leaders would give the UK "a little bit more time" to find a Brexit solution.
"It does not want to leave without a deal at the moment, it doesn’t want to vote for the deal and of course a lot of people, maybe even half the population, don’t want to leave at all.
"So I believe the consensus here in Brussels, and across the European Union, will be to give the United Kingdom a little bit more time for the cross-party talks that are happening to conclude. And we can review the situation then in a few months’ time."