The European Affairs Minister says nobody is going to get everything they want from the Northern Ireland Protocol.
It comes after Foreign Affairs Minister Simon Coveney accused the British government of bad faith as it seeks to renegotiate aspects of the protocol.
London is expected to ask that European Court of Justice judges no longer have a role in overseeing the protocol - a demand Mr Coveney described as something "that they know [the] EU can't move on".
The EU is due to table proposals on Wednesday that aim to ease the number of checks on goods moving from Great Britain to Northern Ireland.
Minister of State for European Affairs Thomas Byrne told Newstalk Breakfast he expects these to alleviate concerns from the unionist DUP.
"But what I do know in terms of the concerns.... from the DUP, practical concerns about trade with Britain, they are I think going to be basically resolved this week - in terms of the proposals that the European Commission puts forward.
"I think that will be a big win for businesses and trade in Northern Ireland".
Minister Byrne says this is about compromise, noting that no one side is going to get everything.
"In Northern Ireland, nobody is going to get everything that they want - we've had the Good Friday Agreement where there's huge compromise on both sides of the divide in Northern Ireland designed to bring people together.
"So nobody - whether it's the EU or whether it's the British government or whether it's parties in Northern Ireland - are going to get everything they want."
He also suggests the issue of the European Court of Justice is more theoretical than anything.
"Nobody in Northern Ireland has ever mentioned the European Court of Justice to Minister Coveney or to me, or to anybody really, as an issue in this particular process.
"What we're focused on and what people in Northern Ireland, business people in particular are focused on, are practical solutions to the challenges that the protocol has laid down".
He says these solutions are around issues such as medicines and customs, while the ECJ "is really a theoretical issue for most people.
"It's there in the protocol as sort of an arbitrator of last resort, but its practical impact I think is more theoretical than real".
And he says the uncertainty around Brexit and the protocol is hurting investment in the region.
"We need more inward investment, and we're not getting enough - part of the reason is because there's so much uncertainty, because people keep changing what the position is and bringing uncertainty to the situation".