Jean-Claude Juncker has signalled that he will offer a last-minute helping hand to Theresa May in her bid to get her Brexit deal passed by MPs – but hinted at deep scepticism in Brussels at her chances of success.

A letter from the European commission president is expected on Monday offering further reassurances to MPs that, should it be triggered, the Irish backstop would keep the UK in a customs union only temporarily.

Speaking in Bucharest, Juncker said talks with Downing Street over the content were ongoing. But he said every effort would be made to find a way to convince parliament to support the withdrawal agreement when it votes on Tuesday.

May’s Brexit adviser, Olly Robbins, has been in Brussels this week to try to secure a meaningful document that could unlock some votes in parliament, but has been faced with officials on the other side of the table who are doubtful anything can be done.

Juncker stressed the limitations the member states had imposed on him at the last summit in November, when they insisted they would not even provide a legal interpretation of the deal to help May, let alone unpick any of the terms of the backstop.

Under the withdrawal agreement, to avoid a hard border on the island of Ireland, the UK would stay in a customs union with the EU unless there was an alternative arrangement, such as a trade deal, that could solve the problem.

Juncker, who was in Romania for the start of the country’s six-month presidency of the European council, called for space to allow him to work out a formula that would suit the prime minister, saying: “Laissez-moi faire.” or “Let me do it.”

“We, the commission and I, are in touch on a constant basis with No 10 Downing Street and we will see what happens between now and Tuesday,” he said.

“We will see what the British legislature decides to do with the texts that have been put forward. I still hope that here will be a deal. I do not like the prospect of a no deal, which would be a disaster, I think, for our British friends and for the continent of Europeans. And every effort needs to be made between now and Tuesday afternoon perhaps to ensure that this important issue can be resolved satisfactorily.”

Asked about the substance of the letter that is expected to emerge from Brussels, Juncker played down expectations of a game-changing intervention.

He said: “What we have said very clearly in council and commission, in full harmony, was that there can be no renegotiation, there can be clarification. But that’s all we are discussing with Downing Street what these clarifications might amount to, that should not confused with a renegotiation with regards to the backstop. Aside from these remarks I think it would be unwise to go into the ongoing discussions.”

In a sign of the sensitivity of the moment, Juncker added: “I could become highly prominent from one hour to the next if I were to enter into the detail of your question – and it is not your concern to have me become less popular on different islands. I will resist the temptation.”

At his weekly press conference in The Hague, the Dutch prime minister, Mark Rutte, voiced the concerns of leaders of countries that would be most affected by the UK leaving the EU without a deal.

“The ball is rolling towards the ravine and everyone is watching it without putting their foot in the way,” Rutte said.

There has been speculation in Brussels of a Brexit summit in late January should the deal be voted down, to see if leaders can offer May a way out of her predicament.

EU officials did not deny that this could be a next step, but suggested they would be led by Downing Street should the deal be voted down. Officials declined to comment on the substance of the assurances, simply reiterating that the deal could not be cut across, but adding: “There is something.”