Solicitor General Robert Buckland told BBC News at Ten: "There's an expectation that a discussion will yield some fruit, and I'm not saying it won't and it could very well end up with a further amendment in the Lords".
The prime minister had faced the prospect of a losing a vote after rebels had indicated their support for a change introduced by the House of Lords to require ministers to report what efforts they had made to secure a customs union.
The government concession is all the more remarkable because of the strength of opposition to the original amendment from ministers.
That said, while the government may have won the battle on customs, the war is still to come.
Both Houses of Parliament must agree on the form of the EU Withdrawal Bill, and if the Lords insist on their amendment then the Commons will again be invited to reject it.
They reassured anti-Brexit MPs that the government would accept some of their core demands to give parliament a meaningful say on the terms of Britain's European Union divorce, including - potentially - a new deadline for a deal to be agreed with Brussels that could make it hard for the government.
Labour's leadership, meanwhile, will be on alert for a potential rebellion after ordering its MPs not to back proposals for a Norway-style agreement with the European Union.
JEREMY CORBYN suffered a mass rebellion by 90 Labour MPs over Brexit as the Commons descended into chaos last night.
May hopes to resolve the border issue with a wider trade deal between the European Union and Britain, but has agreed to the need for a plan B if this is delayed or does not happen.
She said: 'I'll pass over the fact it's going to have a Solidarity tent, which obviously won't have any Labour MPs within it.
Cabinet secretary David Lidington said the Government agreed with the "spirit" of the amendment, which is effectively "a statement of government policy" and said ministers would allow it to pass with a few tweaks to the legal language.
So dizzying and confused is the news coming out of the UK about how the EU-UK relationship could and should work after Brexit, that EU negotiators say they are forced to stand on the sidelines while the British government talks and argues with itself.
Although the vote was technically a victory for May, her political sway appeared severely weakened as two competing wings of her Conservative party bickered over how close Britain ought to remain to the EU.
During Commons exchanges, supporters of the EEA said it would be an economic "lifeboat" for the United Kingdom after Brexit by reducing the disruption to business.
"There are people in this palace, your palace, who are attempting to do everything in their power to overturn that decision and to create a meaningless, toothless, neutered Brexit".
"It buys the Government more time, and has no doubt bought off some of the serious concerns of MPs, but this can't just be a case of kicking the can down the road and forgetting about it".
In a dramatic day of votes on Theresa May's flagship Brexit bill, a bid to give teeth to the Prime Minister's promise of "no physical infrastructure" on the border was waved through successfully without a vote.
He added that Britain has to "accept the consequences" of its June 2016 referendum to leave the EU.