Theresa May will attempt to reassure businesses and Northern Irish politicians by insisting during a visit to Belfast that she can find a way to deliver a Brexit deal MPs can support.

The prime minister is due to chair a cabinet meeting on Tuesday morning before departing for a two-day visit to Northern Ireland to underscore her commitment to avoiding a hard border with Ireland.

She is expected to say: “I know this is a concerning time for many people here in Northern Ireland. But we will find a way to deliver Brexit that honours our commitments to Northern Ireland … that commands broad support across the community in Northern Ireland … and that secures a majority in the Westminster parliament.”

Privately, however, there is scepticism within the government about the possibility of a breakthrough before May returns to parliament to make a statement about her Brexit plans on 13 February. “She’s just burning down the clock,” said one cabinet source.

Downing Street said it was still planning to give MPs the chance to vote on the government’s intentions on 14 February after rumours in Westminster suggested it could be pushed back into the following week. “That’s the deadline we’re working to,” said a government source.

The prime minister’s withdrawal agreement faces a new problem in the shape of a potential legal challenge by one of the architects of the Good Friday agreement.

David Trimble, the leader of the Ulster Unionist party when the peace deal was signed, confirmed that he and others were considering legal action over the backstop provisions in the withdrawal agreement.

He told the BBC Radio 4 Today programme: “We are exploring this possibility and we are concerned at the way in which the withdrawal agreement that our prime minister agreed actually turns the Belfast agreement on its head and does serious damage to it.”

He explained: “The EU has come in this exit agreement [and] stripped a significant number of competencies out of the devolved administration and put in place a number of top-down structures, and a UK/EU body which is going to supervise. The success of the [Good Friday] agreement is largely because it was bottom up.”

While May is in Belfast – where she is also expected to meet party leaders, including those from Sinn Féin – an “alternative arrangements working group”, made up of Conservative backbenchers, ministers and civil servants will meet in Westminster.

A spokesman for the Department for Exiting the EU said the first meeting of the group, chaired by the Brexit secretary, Steve Barclay, had been “detailed and constructive, and the first step of a process to find common ground on the issue of the backstop”.

Attendees included the Treasury select committee chair, Nicky Morgan, the European Research Group’s Steve Baker and the former work and pensions secretary Iain Duncan Smith.

The group was created after Tory MPs from the leave and remain camps came together to promote the Malthouse compromise, which involves a longer transition period while alternatives to the backstop are explored.

Q&A What is the Malthouse compromise? Show The Malthouse Compromise is named after housing minister Kit Malthouse, who brokered cross-party talks between Brexiters and former remainers on a possible way out of the Brexit impasse. The result involves redrafting the backstop arrangement for the Irish border which is so unpopular with Conservative Eurosceptic MPs and the Democratic Unionist party, which props up the government. It would also extend the transition period, set out under the previously negotiated withdrawal agreement, until the end of 2021. The extension is designed to give extra time to agree a new trading relationship. Under the plan, the backstop would be replaced with a free trade agreement with as yet unknown technology to avoid customs checks on the Irish border. If the attempt to renegotiate the backstop fails, the Malthouse compromise proposes what amounts to a managed no deal. The PM would ask the EU to honour the extended transition period, in return for agreeing the £39bn divorce bill and its commitments on EU citizens’ rights. This would give both sides time to prepare for departure on WTO terms at the end of 2021 – or to negotiate a different deal. The compromise is backed by the DUP, the European Research Group of hard Tory Brexiters, and former remainers including Nicky Morgan. However, the EU has repeatedly stated that the terms of the Withdrawal Agreement are not open for renegotiation

Morgan said the government was “taking very seriously the desire of parliament to identify alternative arrangements”.

Meanwhile, senior EU figures have continued to underline their objections to replacing the backstop. The chief Brexit negotiator, Michel Barnier, who held talks with the Dutch prime minister, Mark Rutte, on Monday, tweeted that the withdrawal agreement “cannot be reopened” and the EU was “ready to work on alternative solutions during transition” – in other words, after the UK had left.

The Labour MP Stephen Doughty, a supporter of the anti-Brexit campaign Best for Britain, said: “The alternative arrangements group looks like a colossal waste of taxpayers’ money to create another unicorn plan for peace in the Conservative party. While senior EU and economic experts are already rubbishing the plan, a select group of Tory MPs are simply wasting time on another plan that is already dead as a dodo.”

The Liberal Democrat leader, Vince Cable, warned about the potential impact of a no-deal Brexit on Northern Ireland, after the government conceded it had not specifically earmarked funds for avoiding disruption in the province.

The Northern Ireland minister, John Penrose, told Cable in a written parliamentary answer that his department had not allocated any funding for no-deal preparations, adding: “A number of staff across the department work on both EU exit and non-EU exit related work.”

Cable said: “If the government is serious about letting Britain crash out of the EU, there should be a dedicated unit in the Northern Ireland Office, preparing for this eventuality. We can only conclude that the no-deal threat is a false one.”