The BBC said it hopes “the majority” of post closures will be achieved through voluntary redundancy.
The corporation also said that some programmes on Radio Ulster and Radio Foyle would be “impacted” by the plans.
That includes the daily breakfast news programme on Radio Foyle and the weekly Inside Business programme on Radio Ulster.
The proposals mean most of Radio Foyle’s news output is to be cut, and every radio news journalist role at the Northland Road station is now at risk of redundancy.
However, more money is set to be spent on BBC NI’s online and digital services, including the BBC iPlayer.
Staff and trade unions will now be consulted on the savings plans.
As a whole, the BBC announced proposals to make £500m in annual savings and to become a “digital-led” organisation in May 2022.
That included plans to employ up to 1,000 fewer people in the publicly-funded part of the BBC over the next few years.
Channels like CBBC and BBC Four are to be moved online and a single news will replace separate UK and world channels.
In January 2022, the then Culture Secretary Nadine Dorries confirmed the BBC licence fee is to be frozen at £159 for two years.
According to the BBC’s most recent annual report for 2021/22 the number of adults who watch BBC TV each week has fallen, whereas use of digital services like the iPlayer, BBC online and BBC Sounds has risen.
BBC NI spends about £55m a year on local programmes and services across TV, radio and online.
In a statement BBC Northern Ireland said that its plans “reflect a BBC-wide strategy to prioritise digital content, announced earlier this year, and the need to manage inflationary and other cost pressures”.
“BBC Northern Ireland is proposing to close approximately 35-40 posts to contribute to its £2.3m savings and reinvestment plans,” the statement continued.
“Efforts have been made to limit the effect of proposed changes on the scope and benefits of BBC services in Northern Ireland and local staff teams.”
The interim director of BBC Northern Ireland, Adam Smyth, added that the corporation faced “some difficult choices, none of which are easy”.
“We have to find monies to maintain and develop our local presence on BBC iPlayer and to absorb cost pressures across different aspects of our work,” he said.
“Our concern in all of this will be to safeguard audience value and benefit and to remain mindful of the impact that this announcement will have on BBC staff in Northern Ireland.”
BBC NI had previously scaled back plans for a £77m redevelopment of Broadcasting House in Belfast.
BBC NI also said that other ongoing UK-wide operational and staffing reviews are may also “impact other locally-based teams and roles next year”, but gave no further details about what that might mean.
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