Ministers say they want a "special partnership" with the EU, but it is "neither necessary nor appropriate" for the ECJ to police it.
Critics say the word "direct" leaves room for the ECJ to still play a part.
The pro-EU Open Britain group said the phrase paved the way for a "climbdown" over the jurisdiction of the court.
But Justice Minister Dominic Raab has told the BBC: "We're leaving the EU and that will mean leaving the jurisdiction of the European Court of Justice.
"The likely outcome, is we'll need some form of arbitration."
Arbitration is where disputes are settled by a neutral third party. The UK and the EU would each appoint arbitrators and agree on a third.
He said this would be a process that both sides would have confidence in.
He added this was different to the UK accepting the jurisdiction of ECJ which would be "lopsided and partisan and that's not on the cards".
But Labour MP Chuka Umunna, speaking on behalf of Open Britain, said: "Nothing the government says it wants to deliver from Brexit - be it on trade, citizens' rights, or judicial co-operation - can be achieved without a dispute resolution system involving some role for European judges."
Prime Minister Theresa May has promised to take the UK out of the Luxembourg-based ECJ's jurisdiction after Brexit.
At her party's conference in October 2016, she said: "We are not leaving (the EU) only to return to the jurisdiction of the European Court of Justice. That is not going to happen."
And in January this year, in her Lancaster House speech, she reiterated this, saying: "So we will take back control of our laws and bring an end to the jurisdiction of the European Court of Justice in Britain."
But the question of how future agreements between the UK and the EU will be enforced is proving contentious.
The policy paper will be released later as ministers argue there are plenty of other ways of resolving disputes without the European courts.
The ECJ is in charge of ensuring member states abide by EU law.
Its rulings are binding on all member states, and it also settles disputes between countries and EU institutions.
After the UK voted to leave the EU last year, Mrs May promised to make the UK a "fully independent, sovereign country".
But pro-EU campaigners say the government made an "appalling error" by making leaving the ECJ a "red line" in Brexit negotiations, saying new courts will now be needed in all the areas it extends to, including trade, citizens' rights and security.
Brexit Secretary David Davis, who will resume negotiations with Brussels on 28 August, has spoken of the "arbitration arrangements" that will be needed in areas where the UK and the EU make new arrangements - but insists these will not involve the ECJ.
"If Manchester United goes to play Real Madrid, they don't allow Real Madrid to nominate the referee," he said last month.
Wednesday's publication - the latest in a series of papers setting out the UK government's stance on key issues - will say there are a "variety of precedents for resolving disputes that may arise between the UK and the EU" without the ECJ having direct jurisdiction.
These will need to include the free trade deal the UK hopes to strike with the EU to replace its membership of the single market.
Red lines 'blurred'
Sir Keir Starmer, the shadow Brexit secretary, said: "The prime minister's ideological insistence that there can be no future role whatsoever for the ECJ or any similar court-like body risks preventing the deal Britain needs."
Liberal Democrat leader Vince Cable said Mrs May's "red lines are becoming more blurred by the day", saying the ECJ had "served Britain's interests well" and should not be "trashed".
The Institute of Directors called for "flexibility and pragmatism" when leaving the ECJ's jurisdiction.
"The emphasis here should be on ending its direct effect, not trying to throw off the influence of the court altogether," it said.
On Monday, the president of the court of the European Free Trade Area (Efta) - which governs Iceland, Liechtenstein and Norway's relationship with the single market - suggested his institution could be used.
But this could anger some Eurosceptic Conservative MPs, because the Efta court, also based in Luxembourg, tends to follow closely the ECJ with its rulings.
The ECJ has also emerged as the central stumbling block in reaching a deal on the rights of EU nationals after Brexit.
The EU side believes the ECJ should have a role in enforcing these rights - a proposal rejected by the UK.
The UK government said its paper on Wednesday would offer maximum certainty to businesses and individuals. It will also suggest that dispute resolution mechanisms could be tailored to the issue at stake in each agreement.
"It is in the interests of both the UK and the EU, and of our citizens and businesses, that the rights and obligations agreed between us can be relied upon and enforced in appropriate ways," a spokeswoman said.
"It is also in everyone's interest that, where disputes arise between the UK and the EU on the application or interpretation of these obligations, those disputes can be resolved efficiently and effectively."