Conservative leadership candidate Matt Hancock has proposed an "Irish Border Council" as part of his Brexit plan.
Mr Hancock said it would aim to find a way to maintain a soft border and allow the UK to have an independent trade policy.
He said the council would be chaired by an independent figure, using the example of Senator George Mitchell's role in the NI peace process.
He added that he would also seek a time limit to the backstop.
The backstop is a position of last resort to maintain an open border on the island of Ireland.
It would see the whole of the UK stay in the EU's customs union and Northern Ireland stay in the single market for goods.
It’s time to get real about how to deliver Brexit.— Matt Hancock (@MattHancock) June 2, 2019
My Brexit Delivery Plan is the only credible plan to leave by 31 October.
So let’s deliver Brexit and focus on the future #LetsMoveForward pic.twitter.com/m6jmlVG4Hv
It would apply "unless and until" a deep trade deal or a technological solution, sufficient to keep the border as open is it is now, was agreed.
Mr Hancock claimed the EU has "previously mooted adding a time limit to the backstop".
Mr Hancock said his border council would involve all parties in Northern Ireland and have a role for the Irish government and EU.
He said it would aim to find a "long-term political, administrative and technological solution".
'Build Irish confidence'
The proposal from Mr Hancock has a focus on technology, but he said any solution would require the political will and consent of communities on both sides of the border.
Meanwhile, another candidate - Sajid Javid - has said his Brexit plan also hinges on coming up with an alternative to the backstop.
Speaking on The Andrew Marr Show, he said: "I will focus on the one Brexit deal that has already got through Parliament. That was the withdrawal agreement with a change to the backstop."
He added: "[Ireland] is the tail that wags the dog on this and we need to make sure we can do more to build that goodwill in Ireland and build their confidence.
"What I would do is make a grand gesture to Ireland that we would cover all their costs - the upfront costs, the running costs - of a new digitised border.
"I think it could be done in a couple of years, but I think we could cover their costs."
Later Ireland's Europe Minister Helen McEntee reiterated Ireland's position.
She tweeted a clip of Mr Javid adding the comment: "The Withdrawal Agreement will not change. The backstop cannot change.
"Much of what was in the Withdrawal Agreement was asked for by UK. They were not bystanders in the two years it took to negotiate.
"Bit of realism needed."