Ireland's prime minister Leo Varadkar has said border checks should be moved to airports and ports.
Brexit: Ireland calls for sea border with Britain
The Irish government has called for a sea border to exist between Britain and Ireland after Brexit, in the latest development in Theresa May's European Union negotiations.
Ireland is the only country which shares a land frontier with Britain, however, no controls currently exist between the north and south of the island of Ireland.
Politicians in Dublin, Belfast and London have all said they are opposed to the return of a "hard border" between Britain and Ireland for fear of jeopardising the 1998 peace process.
Mrs May had proposed to use technology such as surveillance cameras at the border to allow continued free trade between Britain and Ireland after Brexit in 2019.
However, according to The Times, last week Irish Prime Minister Leo Varadkar said any customs and immigration checks should be moved away from the land border to airports and ports, which would in turn create a sea border between the two nations.
On Friday, Irish foreign minister Simon Coveney also rejected the plans for a technical solution and called on the British government to come up with other options to deal with the border issue.
He tweeted: "IRE can't support proposals resulting in border checkpoints - UK decision to leave EU, we need imaginative solutions."
The proposal of a sea border has been rejected by both Britain's chancellor Phillip Hammond and the Conservative Party's minority government allies, the Democratic Unionist Party.
"The Irish government, the British Government and indeed the European Union Commission all share an ambition to ensure that we do not reinstate any kind of hard border between Northern Ireland and the Republic of Ireland," Mr Hammond told Sky News.
"That is a very high priority to us because the peace process in Ireland is extremely important to us. But the answer on how to deliver that cannot be to create a border between Northern Ireland and Great Britain."
While DUP chief whip Sir Jeffrey Donaldson said that Dublin's proposition was "absurd and unconstitutional".
He told the BBC Radio 4's Today programme: “I think Dublin is being too pessimistic and I suspect that behind this is a little bit of politics going on which is unhelpful.
“There is no way that the DUP will go for a border like this. Dublin really needs to understand that that proposition is absurd and unconstitutional."