The EU is prepared to change its Brexit position if Theresa May softens her negotiating red lines, Michel Barnier has said.

The offer from the EU’s chief Brexit negotiator could be seen as a strategic olive branch coming just as the prime minister tries to strike a deal between the warring sides of her cabinet at Chequers.

“I am ready to adapt our offer should the UK red lines change,” Barnier said in a speech to the Institute of International and European Affairs in Brussels. “Our objective has always been to find an agreement with the UK, not against.”

He called on all sides to stop arguing over the Irish border, imploring everyone to “de-dramatise” the issue.

However, he said the EU would not shift its own red line on the single market, which he said was “not and never should be seen as a big supermarket; it is economic, cultural and social life, it should be developed in all its dimensions”.

He added: “The single market is our main economic public good. We will not damage it. We will not unravel what we achieved with the UK. We must find solutions that respect the integrity of the single market.”

This may douse any hopes that the prime minister could emerge from Chequers on Friday night with a package that simultaneously unites the cabinet and is acceptable to the EU, which has always said access to the single market is conditional on the UK accepting freedom of movement of people.

Hardline Brexiters were horrified to learn that May was preparing to soften her red lines by asking for access to the single market for goods, but not services, and will see Barnier’s comments as confirmation that the EU will not countenance a special compromise for Britain on immigration.

However, the conciliatory tone of Barnier’s speech was striking and may help move negotiations to the next phase. On Northern Ireland, he repackaged the need for a backstop solution, spelling out the need for regulatory alignment for livestock and agri-food. He said this was necessary for food safety and animal health across the border and would allow farming to continue as it does.

“We must all de-dramatise this backstop, we need to clarify how and where these controls are done, but ultimately [they are] only technical control on goods, no more, no less,” Barnier said.

“Our own backstop solution would mean the limited set of EU rules would continue to apply in Ireland as it does today, which means there would be no need for checks at the border.”

He again warned that the clock was ticking and the EU needed to see “realistic and workable solutions” from the UK.

For the first time he conceded there was still work to be done on protecting the rights of British citizens living in the rest of Europe and non-British EU citizens in the UK.

“There are four or five million citizens for whom Brexit is a constant source of worry [about] whether they can continue living their lives with the same rights for the rest of their lives. This is not the end of the road and we need to remain vigilant,” he said.