The plans would see the broadcaster do away with local news and programmes during the day, with the exception of breakfast and drive-time shows, and replacing them with content from BBC Radio 5 Live.
The proposals could involve many of the BBC's 40 local radio stations being closed, with 700 jobs at risk, according to the NUJ.
The union's general secretary Jeremy Dear warned that the proposals would "rip the heart out of local programming".
"Local radio plays a crucial role in keeping local communities informed. These proposals would rip the heart out of local programming and effectively sound the death knell for local radio."
The BBC countered the NUJ's claims in a statement issued today: "No decisions have been made so it would be wrong to speculate. It is of course only right that BBC staff have an opportunity to input ideas about shaping the BBC's future.
"The DQF (Delivering Quality First) sessions are designed to provoke discussion amongst staff about the way the BBC works and any decisions coming out of the process would be subject to approval by the BBC Trust."
BBC local radio, which broadcasts Radio 5 Live overnight, has already increased the networking of news and programming for some stations. Drive-time news and programming has recently been networked for BBC Sussex, BBC Surrey and BBC Kent, with one drive-time show broadcast across the three stations.
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