BBC News NI understands that the government's latest financial offer to the Stormont executive now stands at £1.5bn over the next three years.
On Monday, Northern Ireland Secretary Sir Chris Bryant visited Stormont and made an initial offer of £350m per year over the same period to help stabilise the executive's finances - a £1.1bn package.
Executive parties rejected that and said the government would need to increase its contribution in order for Stormont to balance its books this year.
It is believed that the majority of the money for each year would be available to the executive for day-to-day (resource) spending, with some money required to be set aside for longer-term (capital) projects.
It is understood budget discussions on Friday morning are taking place virtually.
Speaking ahead of the meeting, Stormont's Education Minister Paul Givan had said he was "confident" of a revised financial offer from the government on Friday, but did not believe it would go far enough to resolve the budget deadlock.
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Givan said the executive should "not be rushed" in terms of signing up to a financial deal.
"I will be engaged in this process for as long as it takes," he told BBC's The View programme on Thursday night.
It is understood the NI Secretary wrote to parties on Thursday ahead of the meeting.
![Education Minister Paul Givan said the executive should "not be rushed" in terms of signing up to a financial deal [PA Media]](https://s.yimg.com/lo/mysterio/api/feb5c1666b211c7bf6bc32a31f01da8a44f084976b04affd927868a1d279ee6c/lightyear_networkapi/resizefill_w960%3Bquality_80%3Bformat_webp/https%3A%2F%2Fmedia.zenfs.com%2Fen%2Fbbc_us_articles_995%2F71f839d4a83402428d39b6e28cc7c0dc.jpg)
Sinn Féin's Chris Hazzard told The View that there remained a "live negotiation" and that the funding needed to be increased.
He added that the Treasury had "taken too long" to start discussions with the executive and had put parties in a difficult situation.
Following the passing of a deadline in August, Stormont officials were given legal powers to spend up to 95% of last year's funding in the absence of ministers agreeing the budget.
Last week, Prime Minister Andy Burnham pledged to get the Stormont government functioning properly with a budget.
![On Monday Sir Chris Bryant visited Stormont to make an offer to the executive [PA Media]](https://s.yimg.com/lo/mysterio/api/ca81255c018d032e9ffd5acb4532e330b1fd5e1452332b1d8f3c33d8848df9a2/lightyear_networkapi/resizefill_w960%3Bquality_80%3Bformat_webp/https%3A%2F%2Fmedia.zenfs.com%2Fen%2Fbbc_us_articles_995%2Ff7a40d6d0133ae05b1d9ba20a6fb2ca1.jpg)
No formal deadline has been set in the talks with Westminster, but Number 10 is due to publish its budget on 28 October so there is an expectation from some Stormont sources that any financial settlement should be agreed before then.
Alliance assembly member (MLA) Kate Nicholl said her party had urged the government to make reform of the Stormont institutions a condition, as part of any overall deal on the budget.
Ulster Unionist leader Jon Burrows said the executive was discussing "significant" sums of money, but also refused to be drawn on an exact figure.
He said there was an aspiration to agree a budget soon, but it needed to be done properly.
SDLP MLA Matthew O'Toole, Stormont's leader of the Opposition, said with every day that passes without a budget, public services are suffering in Northern Ireland.
![First Minister Michelle O'Neill says Westminster "need to fix the baseline" [Reuters]](https://s.yimg.com/lo/mysterio/api/4e6286b1c79aa777a1f62775ccb21c8789b1877bcb5466bb61c28ee4a4efc0d0/lightyear_networkapi/resizefill_w960%3Bquality_80%3Bformat_webp/https%3A%2F%2Fmedia.zenfs.com%2Fen%2Fbbc_us_articles_995%2F3b2557bbcc8d4cdfde3045e4498add78.jpg)
The executive has repeatedly said it cannot agree a budget for this financial year without extra support from Westminster.
Speaking after meeting the secretary of state on Monday, First Minister Michelle O'Neill said the executive was now in a "negotiation" with the government.
"We get to this juncture time after time, crisis point after crisis point - they need to fix the baseline.
"If they throw a few pounds on the table and walk away we'll end up back in this scenario."
DUP leader Gavin Robinson said the initial offer from the government "falls well short of even some of the pressures in one department, let alone across the Northern Ireland Executive".
"Anybody who says we just need to get on and agree this can explain the cuts that will come as a consequence," he added.