As part of a plan, put forward by party leader Jeremy Corbyn, a Labor government would strike a new Brexit deal with the EU and then put it to a public vote. There would be an option on the ballot paper to remain.
But the strategy threatens to put Corbyn and the NEC on a collision course with leading front-bench Labor members, including shadow foreign secretary Emily Thornberry.
Thornberry has called on Labor to make a clear statement now that it wants Britain to remain in the EU.
The Times in London quoted Thornberry warning that Labor would lose 30 percent of its vote at the next general election unless it adopted an unambiguous pro-Brexit stance.
Thornberry said the party would haemorrhage support to minority parties unless it campaigned against Brexit.
She was backed by London's Labor mayor Sadiq Khan who said Corbyn must get party managers to get Labour MPs in the House of Commons to campaign to remain in the EU.
The crunch will come Monday when thousands of delegates at the conference vote on what the party's Brexit policy should say.
The minority Liberal Democrats has already voted at its conference to make its election pledge to keep Britain in the EU if it wins.
If Labor does back a policy that could keep Britain in the bloc, it will be seen as the party going head-to-head with Boris Johnson's Conservative Party that has pledged to leave the EU with or without a deal on Oct. 31.
The battle over Brexit at the Labor conference dominated the headlines Sunday in the on-line stories for Britain's main newspapers.
The Guardian's headline read: "Corbyn heading for clash with Labor members by calling for Brexit decision to be postponed".
The Guardian reported that the party's NEC shows that Corbyn's current plan is for a Labor government to negotiate a new Brexit deal within three months of coming to power and then to hold a new referendum. The party would decide at a one-day special conference after the renegotiation on how it would campaign in the new referendum.
Prime Minister Boris Johnson, meanwhile, arrived in New York Sunday with plans Monday to meet European Council President Donald Tusk, as well as German Chancellor Angela Merkel and French President Emmanual Macron.
Media reports in London said they are likely to discuss a series of ideas put forward Thursday by Britain in a bid to break the current Brexit deadlock.
"This gives the Prime Minister an opportunity to talk to them at leader level about what some of our proposals are," a government spokesperson said in London.
The leaders have travelled to the U.S. for a meeting of the United Nation's General Assembly, but talks on Brexit are expected to take place on the sidelines.
Johnson is also expected to learn Monday when the British Supreme Court will announce its decision on whether he acted unlawfully by suspending the British parliament for five weeks. The court's president announced Thursday the decision would be announced early in the coming week. Some newspapers in London suggested Sunday that the result could be announced as early as Monday, Sept. 23.