Theresa May will visit Northern Ireland to give a speech on Brexit policy and meet business leaders on Tuesday.
The prime minister is expected to underline the UK's commitment to ensuring there will be no hard border.
She is due to try and reopen negotiations with the EU on the withdrawal deal, with a view to an alternative to the backstop.
However, Tánaiste (Irish Deputy Prime Minister) Simon Coveney said none of the ideas have "stood up to scrutiny".
He said that "some at Westminster" were asking Ireland to "do away with an agreed solution" between the UK government and EU negotiators and "replace it with wishful thinking".
He added that it was an unreasonable thing to ask of the Irish government and that he expected the UK government to follow though on its commitments.
The Dutch foreign minister, speaking from the Irish border during a visit on Monday, said it was "not reasonable" to expect there will be a completely different outcome to what has already been negotiated.
The backstop is an insurance policy, designed to avoid a hard border "under all circumstances" between Northern Ireland and the Irish Republic.
It was part of the original withdrawal deal, agreed between the UK government and the EU.
However, with the withdrawal deal having been rejected in parliament for reasons including objections to the backstop, Mrs May will now try and renegotiate the deal with the EU.
Previously, Mrs May had encouraged Northern Ireland businesses and farmers to get behind the backstop she had negotiated with the EU in order to avoid disruption to cross-border trade after Brexit.
Labour MP Keir Starmer, speaking in Belfast on Monday, said a backstop was an inevitable part of a Brexit deal.
Sir Keir, his party's Brexit spokesperson, said he had real concerns about the current backstop but that some version of it remains necessary.
He said he believes a combination of the UK being part of a customs union with the EU and aligning with the regulations of its single market can secure the UK economy.
He added it would ensure there was no hard border on the island of Ireland.
Sir Keir wants the prime minister to hold another Commons vote on the customs union proposal.
'Not reasonable' to expect different deal outcome
by John Campbell, BBC News NI economics editor
The Dutch foreign minister has said the EU is willing to listen to "specific proposals" on the Brexit backstop but so far none have been made by the UK.
Stefan Blok was speaking on a visit to the Irish border on Monday.
He said it was "not reasonable" to expect there will be a completely different outcome to what has already been negotiated.
He was joined on the border by Ireland's Europe Minister Helen McEntee.
She said the backstop was needed to protect peace and the all-island economy.
She called on the UK government to live up to its commitments.
A group of MPs, including Brexit Secretary Stephen Barclay, and government officials are discussing alternative arrangements to the Irish backstop.
The Alternative Arrangements Working Group, consisting of Leave and Remain MPs, is holding three days of talks from Monday.
Sir Keir said it was unlikely this approach would work at this late stage in the Brexit negotiations.
He added that the prime minister's change in policy had raised anxiety levels in Northern Ireland.
Meanwhile, the UK government has announced it has agreed a deal with the Irish government over social security arrangements for UK and Irish citizens living and working in each other's state.
The agreement is part of the commitment to maintain the rights associated with the Common Travel Area, the UK government said.
What is the backstop?
The backstop is an insurance policy to ensure no hard border on the island of Ireland and would kick in if, two years after the Brexit, the UK and the EU cannot reach a trade agreement that avoided the need for physical border checks.
It would keep the UK in the "single customs territory" with the EU and leave Northern Ireland effectively in the EU's single market for goods.
Critics fear the UK could be "trapped" in this arrangement for years, while Unionist MPs in Northern Ireland also fear it would divide Northern Ireland from the rest of the UK.
Parliament rejected the original withdrawal agreement over objections to the backstop.
Mrs May will now return to the EU and try to renegotiate the deal. However, the EU has said it will not reopen talks on the backstop.