The EU is preparing to help Theresa May build a parliamentary majority for a Brexit deal by offering Downing Street a written commitment to think again about “frictionless trade” if the UK changes its red lines after it leaves the union.

EU leaders want to throw the prime minister a lifeline in their long-awaited political declaration on a future deal, a first draft of which is expected next week.

The four to five page declaration is expected to include an “evolution clause” in which the EU will say it remains open to improving its offer should a British government change tack during the 21-month transition period.

EU officials hope that, despite the opposition of a large number of Tory and Labour MPs to a Canada-style agreement which would create barriers to trade, May will be able to garner enough support in parliament for a deal if it is clear that the declaration is not the last word on the future relationship.

During a recent meeting in Brussels with the EU’s chief negotiator, Michel Barnier, Jeremy Corbyn was told that supporting a Canada-style free trade deal now would not bind the hands of a future Labour government, diplomatic sources have told the Guardian.

Labour has said it will vote against any free-trade agreement that erects barriers to trade through regulatory and customs checks. The prime minister is likely to need the support of a large number of Labour MPs to get any deal through parliament given the division within her own party.

Barnier has also appealed to MEPs to talk down the possibility of an extension of the two-year negotiating time allowed under article 50 of the EU treaties, in an attempt to pressure parliament into supporting a deal.

Earlier this week, the European parliament’s Brexit coordinator, Guy Verhofstadt, expressed his opposition to any prolongation of the talks.

The EU’s commitment to improve its offer at a later date is being drafted into the EU’s political declaration spelling out the terms of the “Canada +++” offer.

The document will say that the EU’s offer of a tariff- and quota-free deal on imports and exports will still involve new customs and regulatory checks because of the UK’s decision to leave the single market and customs union. It will add, however, that “if these positions were to evolve, the union will be prepared to reconsider its offer”.

Mujtaba Rahman, a former treasury and European commission official who is now head of Europe for the Eurasia Group risk consultancy, said the clause reflected the ongoing debate within the EU over how hard it should be on the terms of a deal.

Similar language was used in March in guidelines produced by Donald Tusk, the European council president, in a manoeuvre designed to avoid closing off options that could be available in the future.

“It seems that the same trick is being used again,” Rahman said. “The idea is to say that a more ambitious future is possible. There is debate about how hard they should be now and whether options should be closed off. This is an acknowledgement that political space could open up for a more ambitious deal later.”

Barnier is known for brandishing a picture to illustrate how the UK’s current decisions on the single market and customs restrict the EU’s offer, with descending steps associated with different countries’ levels of access to the EU single market.

An EU source said: “The message to Labour is that the UK could move up Barnier’s stairs if the British government changes its position in the transition period. Voting in favour of the deal now would not be the last word on it.”

A senior EU official told the Guardian that such a clause “would suit the EU and suit the UK”, by ensuring that neither side was boxed in. A European commission spokesman declined to comment on “ongoing negotiations”.

The Guardian understands that Barnier was encouraged by May’s failure to name-check the Chequers proposals during her party conference speech in Birmingham.

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The EU has rejected the central planks of the prime minister’s white paper: a common rulebook on goods, and a customs arrangement that would avoid checks on goods while allowing the UK to pursue an independent trade policy.

However, the political declaration is also likely to contain a pledge to build a “free trade area” with the UK, to the extent to which the British government’s stance allows, in a nod towards the intention of building a deep and unprecedented trading relationship. An EU diplomat said: “Maybe it is just language, but that’s what is important at this political stage.”

Confidence that diplomatic language over trade in the declaration can make it palatable to Downing Street is not yet matched over the issue of avoiding a hard border between Ireland and Northern Ireland.

The UK committed to agreeing to a “backstop” solution for avoiding a hard border, which would be put in place until a future trade deal or technical solution could resolve the problem.

The British government has so far proposed a temporary customs arrangement, under which the whole of the UK would in effect stay in the customs union for a restricted period.

However, an EU official said: “The temporary customs arrangement is dead. They need to build on that. But even a customs union on a temporary basis is a problem. And we have heard what the DUP [Democratic Unionist party in Northern Ireland] say about anything that is not UK-wide. It is going to be a tense two weeks until the leaders’ summit.”