Political representatives gathered to discuss the ongoing stalemate following a meeting between the executive and Sir Chris Bryant, who travelled to the region on Monday.
Prime Minister Andy Burnham previously committed to ensuring the Stormont administration operates effectively through a budget, yet specific figures regarding available funds remain undefined.
Sir Chris engaged in discussions with the executive regarding the financial matter, while also consulting party leaders on possible institutional changes.
Before meeting group representatives, he held separate conversations with each of the five largest political groups individually.
The precise amount of money that might be made available by Westminster has not yet been determined.
Sinn Féin contends that if a major party declines to nominate for an executive role, another party should have the chance to fill that position instead.
Both Sinn Féin and the DUP have historically exercised this nomination power, which smaller groups at Stormont have previously criticised as problematic.
The current administration stated it cannot finalise a budget for the current financial year without further assistance from the Westminster government.
After an August deadline passed, officials were granted legal authority to utilise up to 95% of last year's funding if ministers failed to agree on a new budget.
Alliance and the SDLP have long advocated for changes to power-sharing structures to prevent future collapses.
The nomination process dictates that if the largest unionist or nationalist party refuses to nominate, an executive cannot be formed.