Ireland's EU Commissioner Phil Hogan has said there is "movement" happening on both sides of the Brexit negotiations.
Mr Hogan said if there was a return to the Northern Ireland-only backstop then any constitutional issues in terms of Northern Ireland's place within the United Kingdom that arose could be "improved upon".
He also said the north-south dimension of the Good Friday Agreement could also be used to provide further "oversight" of how a Northern Ireland-only backstop operated.
He did not go into specific detail but said that the Withdrawal Agreement already provided reassurances and oversight for both sides.
Speaking to RTÉ News, Mr Hogan said: "There are constitutional issues that are already in the Withdrawal Agreement that might have to be improved upon if this is a request that's made. Of course we can look at it.
"Also we have to have the north-south dimension in the context of the Good Friday Agreement and if there is oversight needed there I'm sure we can look at it."
He added that the question of how and where checks might apply on the island of Ireland in a no-deal situation was currently "hypothetical" while negotiations between London and Brussels continued.
Speaking following his confirmation as the European Commission's proposed new trade commissioner, Mr Hogan said there had been a "very good" meeting yesterday between Taoiseach Leo Varadkar and British Prime Minister Boris Johnson.
"I also note that the British prime minister has moved away from his position … where he's now prepared to look at divergence of certain rules and regulations on the island of Ireland vis-a-vis the United Kingdom.
"So I think there's movement happening on both sides. Let's see over the next four weeks how we can advance those intensive negotiations to reach an agreement."
Mr Hogan said that the Withdrawal Agreement would not be changed in "a major way".
"The EU has said all along that it's prepared to look at additional text and additional ideas in the political declaration, but also have been very strongly saying that the Withdrawal Agreement that has been agreed remains as it is, with the caveat that if you want to go back to the Northern Ireland-only backstop, which gives security to the island of Ireland, [provides for] the protection of the Good Friday Agreement, gives frictionless trade and no hard border, equally it would give Mr Johnson … an independent trade opportunity to do trade deals around the world."
Pro-Brexit MPs, including Mr Johnson, have long complained that the existing UK-wide backstop would prevent the UK from having an independent trade policy, possibly indefinitely.
Mr Hogan said that if there was a hard Brexit at the end of October it would not be the same as a "clean break Brexit".
"The UK political system seems to be under the misplaced notion that actually if you crash out of the European Union you have dealt with all the issues.
"In fact the work only starts again, like…citizen's rights, in relation to payments to the EU, in relation to the GFA and the island of Ireland issues. The issues remain."
Mr Hogan warned that in the event of a no-deal Brexit it could take up to eight months before negotiations on a future trading relationship could begin.
"We [would] have to get a mandate then as a Commission from the member states of the European Union to negotiate a Free Trade Agreement. That could take some time. It could take six to eight months before all member states have come to a conclusion about the mandate for an EU-UK Free Trade Agreement."
Mr Hogan said the question of where and how checks on the island of Ireland would apply in the event of No Deal was "hypothetical".
"This is part of the negotiations," he said. "Checks and controls will be largely dependent on where a deal is going to be reached. So we're not going to be hypothetical … until such time as we see are we going to have a NI-only backstop, which means we won't have this problem, and if we do have a different type of agreement we're going to have to decide who is going to do the checks and where they have to be done.
"But everybody has agreed there isn't going to be a hard border in the context of the old traditional mechanisms we had in the past, where customs and checks had to be done on the border between Northern Ireland and the Republic of Ireland.
"We're going to find a way in order to do these issues at the point of origin and point of destination. Also we must be mindful of the fact that 55% of all imports into Northern Ireland from the UK come through Dublin where they [will be] automatically checked."
Elsewhere, DUP chief whip Jeffrey Donaldson warned that unionists will have to be on board if there is going to be a deal on Brexit.
Speaking on RTÉ's Prime Time, Mr Donaldson said that he welcomed the comments of Mr Hogan over the "penny beginning to drop" that pragmatic solutions could be introduced into the Brexit debate at the final hour.
He also welcomed comments by Taoiseach Leo Varadkar and Fianna Fáil leader Micheál Martin, describing them as "significant comments, recognising that unionists have valid concerns that need to be addressed".
"And if we are going to get a deal, unionists have to be on board for that."
Speaking after a meeting between the DUP party and PM Boris Johnson at Westminster, Mr Donaldson dismissed the suggestion that Conservative supporters were willing to sacrifice Northern Ireland's place in the UK if it meant securing Brexit.
He said: "The principle of consent means that it is for the people of Northern Ireland to decide whether we leave the UK or not. That won't be a decision with respect taken in Yorkshire or London."