BBC director general Mark Thompson will meet union leaders later to discuss his planned shake-up of the corporation.
BBC Trust chairman Sir Michael Lyons has said "public concern" might mean the corporation will have to "rethink" plans to axe two radio stations.
The strategy announced on Tuesday earmarks digital radio stations 6 Music and Asian Network for closure, and would scale back the BBC website.
There has been growing opposition to the announcement by director general Mark Thompson on Tuesday, earmarking 6 Music and Asian Network for closure.
Broadcasting union Bectu and the National Union of Journalists fear up to 600 jobs could be lost.
The proposals will go through a public consultation before being approved.
Mr Thompson says compulsory redundancy would be kept to a minimum. The plans are to go through public consultation.
Mr Thompson is expected to meet with union leaders later, who say 600 people could lose their jobs.
Under the strategic review, which scraps the BBC Switch and Blast! brands aimed at teenagers, the corporation would divert nearly £600m a year towards programme-making.
There has already been talk of staff strikes to fight any compulsory redundancies.
Spending on imported programmes and films would be cut by 20% to be capped at no more than 2.5p in every licence fee pound, with spending on sports rights to be capped at 9p in the pound.
The proposed cuts have been criticised by music industry figures including music producer Mark Ronson and pop star La Roux.
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The review, which has been submitted to the BBC Trust, said more money will be ploughed into international news, with the corporation concentrating on making "fewer things, better".
However, NUJ general secretary Jeremy Dear said ahead of Wednesday's meeting: "We'll be making the point that we don't believe it is justified for jobs to be cut.
"We don't believe it is justified to cut 6 Music and the Asian Network. If they press ahead with those plans, they are putting themselves on a collision course with the unions."
Mr Thompson unveiled his strategy after months of criticism from commercial rivals that the BBC was becoming too large and encroaching on competitors' markets.
Meanwhile, a report in the Daily Telegraph suggests that should the Conservatives gain power in this year's general election, they would force the BBC to reveal the salaries paid to its top stars.
The review set out plans only to disclose the total paid to its top-earning entertainers.
Fans' protest
According to the Telegraph, the chairman of the BBC Trust, Sir Michael Lyons, has admitted the corporation is prepared for a reduction in the licence fee.
Bectu general secretary Gerry Morrissey has said the cuts proposed in the review are "purely politically motivated", and claimed the BBC had been "bounced by its competitors".
However, the BBC's media correspondent Torin Douglas said: "The BBC's critics say the cuts don't go far enough and, with the public about to be asked their views, the debate is only just beginning."
Almost 100,000 people have joined a Facebook campaign to save 6 Music, which attracts nearly 700,000 listeners a week.
BBC 6 Music presenter Jarvis Cocker has spoken out against the plans
Presenter Jarvis Cocker has added his opposition to the plans.
He said: "As far as I can see, a station like Radio 6 is perfectly in the spirit of what the BBC was supposedly set up to do - public service broadcasting.
"It's airing music that wouldn't get heard otherwise."
The proposed cuts have been criticised by music industry figures, with the heads of the British Phonographic Institute and the Association of Independent Music saying they were "surprised and alarmed" by the reports.
Liberal Democrat culture spokesman Don Foster said that while the review signalled the end of the BBC "roaming wherever it fancied", he feared the stations earmarked for closure were "sacrificial lambs".
Shadow culture secretary Jeremy Hunt added that he was pleased the BBC was "taking a long, hard look at exactly what it should be doing, but the truth of the matter is that we need to see actions not words".
Mr Thompson has said the earliest 6 Music and Asian Network would close would be the end of 2011.
