The Stormont executive has stated it cannot balance the books without further assistance from Westminster.
Without an agreed budget, public sector workers in Northern Ireland are unable to receive long-awaited pay awards that they are entitled to, matching their counterparts elsewhere in the United Kingdom.
While executive parties acknowledged this position, they argued significant gaps remain before a deal can be agreed upon to allow them to set a budget.
In the absence of an agreed budget, public services have been running under contingency arrangements permitting departments to spend up to 95% of last year's funding.
Hospital doctors have announced plans to strike next month over the issue, while the Royal College of Nursing is currently balloting for industrial action.
Sir Chris held brief virtual discussions with parties last Friday, though it is understood Thursday will see a series of meetings between him and party leaders.
The current package proposed would be split into three tranches with £525m available this year, yet Stormont parties claim this falls short of their requirements.
Sir Chris has suggested the absolute deadline for reaching a deal is January because at that point the money available to departments to spend under emergency arrangements will run out.
Stormont departments are facing a shortfall of up to £1.6bn, according to a spending watchdog.
Last month, Sir Chris made an offer of a financial package worth about £1.5bn over the next three years.