Lord Hain called on Theresa May to keep the UK within the customs union despite the Prime Minister already vowing to bow out of the trade bloc.
Speaking on Sky News, the Labour peer said the Government has failed to “come up with any concrete practical answers” with regards to the border between Northern Ireland and the Republic of Ireland.
He said: “It’s only now for the very first time that the Irish Republic will be in a different place as regards to the European Union from Northern Ireland, Northern Ireland would be out [of the EU] if Brexit happens as planned and the Republic of Ireland would be in – that’s never been the case before.
“The Government’s not yet come up with any concrete practical answers to this, though it is being reported that something is imminent, in which case, by all means, let’s look at it.
“Though I don’t see unless at least Northern Ireland, and ideally the United Kingdom, stays within the customs union – you can leave the European Union you can be within the customs union.”
Lord Hain said remaining in the customs union would allow people to travel across the border as people currently do.
He said: “It allows free trade and economic movement across the border as well as allows people to cross too and I don’t see how if you’re outside the customs union and comply with European rules, how you can actually find a solution to this impenetrable problem otherwise.”
The comments come despite reports Theresa May will offer free movement to Irish citizens in and out of the UK after Brexit.
The arrangement will reportedly restore the Common Travel Area, a special zone between Ireland, the UK, Isle of Man and Channel Islands.
It is understood that after Brexit, EU nationals will be able to go to Ireland on holiday and not show passports to get into the UK.
However, they will not be allowed to work in the UK without a work permit.