The DUP, the dominant pro-UK party in Northern Ireland, effectively has a veto on any deal Prime Minister Boris Johnson puts to the House of Commons, the lower chamber of legislation, Efe news reported.
"We have been involved in ongoing discussions with the government. As things stand, we could not support what is being suggested on customs and consent issues and there is a lack of clarity on VAT," a statement from DUP leader Arlene Foster and the party's Commons leader, Nigel Dodds, said.
"We will continue to work with the government to try and get a sensible deal that works for Northern Ireland and protects the economic and constitutional integrity of the UK.
The pound fell 0.5 per cent after the announcement.
The DUP's consent to a deal is crucial if Johnson is to stand any chance at wielding a parliamentary majority.
How to maintain a soft border between Northern Ireland and the Republic of Ireland is one of the main stumbling blocks in the Brexit negotiations.
The Irish backstop, an insurance policy written into Theresa May's withdrawal deal, would have kept the UK territory in some sort of EU customs union to avoid checks, but it was unpopular among Brexit supporters in the Commons.
Johnson's proposed alternative would keep Northern Ireland in parts of the single market but pull it out of the customs union with checks hypothetically taking place in the Irish Sea, an idea the DUP has previously rejected.
The PM is hoping to get a deal agreed during the European Council meeting taking place over the next two days.
If he fails, he will be legally obliged to seek an extension.
Speaking before the summit, Germany's Chancellor Angela Merkel said there was still no deal but insisted the EU would continue to the last minute to find an agreement.
"There's been movement in recent days and the UK side has shown it is willing to negotiate."
Any deal Johnson lands will still have to pass through the House of Commons.
( With inputs from IANS )