Former Northern Ireland Secretary Lord Hain says he will be tabling an amendment on keeping an open border, in the interests of 'the peace process', as peers debate the Brexit bill.
The Brexit bill passed the House of Commons earlier this month.
However, the government does not have a majority in the House of Lords.
Lord Hain said it was essential to have an open border between Northern Ireland and the Republic of Ireland.
He said he was insisting on an amendment in order to maintain the "peace process and the strength of the economy".
"My amendment is seeking to say you keep that border open, you find a solution, and that should be the condition on which the process of triggering Brexit is set up," he said.
MPs have already backed the proposed law, authorising Prime Minister Theresa May to inform the EU of the UK's intention to leave.
The government does not have a majority in the House of Lords where a record 190 peers are due to speak over two days.
The sitting was extended to midnight on Monday to allow more peers to speak and the debate will continue on Tuesday.
Opposition and crossbench peers are seeking guarantees about the rights of EU citizens in Britain and the role of parliament in scrutinising the process.
Mrs May has said she wants to invoke Article 50 of the 2009 Lisbon Treaty - the formal two-year mechanism by which a state must leave the EU - by the end of March, and the government has warned the House of Lords not to frustrate the process.