The Democratic Unionist Party (DUP) wants a "seismic" offer from Rishi Sunak in order to return to power-sharing in Northern Ireland.
The Stormont assembly has been unable to sit for more than a year, as the DUP refuses to accept the post-Brexit settlement.
Even the Windsor Framework, the renegotiated deal agreed between Mr Sunak and the EU, was unable to convince unionists to return to power-sharing.
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The DUP says the framework does not address their concerns and the party leadership say they want further legislative changes from Westminster.
The collapse also came after the sixth election in five years, which saw Sinn Fein become the largest party ahead of the DUP.
The UK government and the DUP have been in negotiations over the summer, and Northern Ireland Secretary Chris Heaton-Harris insists progress has been made.
Edwin Poots, who briefly led the DUP in Stormont last year, was speaking to the BBC on Sunday morning.
He said: "I think that we need to see something seismic coming from Downing Street and it's going to take something significant to make that happen.
"I very much want it to happen. However, what has been on the table heretofore is nowhere near adequate to bring the DUP back into the room."
Other parties at Stormont, including Sinn Fein, have been calling on the DUP to return to the assembly.
Northern Ireland is currently being run by a mixture of civil servants and ministerial direction from the government in Westminster.
Michelle O'Neill, who would be the first minister if Stormont returned, said last week that the DUP was blocking power-sharing for something "impossible".
"Clearly, we know that the DUP are in negotiations with the British government, but they have been for some time, and they need to get on with it because while they are sitting off trying to maybe achieve something that is impossible, the public are suffering," she told the PA news agency.
She added: "I hope that we can get a resolution. I believe in a restored executive.
"I think that we've been far too long out of the executive. But I hope that we can get to a point where the DUP do end that blockade and get into the executive with the rest of us.
"I think the investment conference this week shows that we have huge economic potential to create more and better jobs.
"But we need an executive up and running to really harness that."