The weekly show, which is currently shown on BBC2 on Friday nights, is presented by Kirsty Wark and Martha Kearney.
As part of a wider shake-up of arts programming, the show looks likely to have its status changed in the coming months.
The show, which has regular panellists and recently featured comedian and actor Billy Connolly and leading novelist Ian McEwan, seems to have lost out in a shake-up of cultural programming.
It will still be shot at the Pacific Quay headquarters of BBC Scotland in Glasgow and its place in the main UK BBC schedules is likely to be filled by other arts programmes.
Jonty Claypole, the BBC's head of arts programming, who is based in Scotland and organises its output from Glasgow, is keen to commission new output.
The BBC has aimed to increase network television production in Scotland to 8.6% of the total by 2016.
However, it has announced Lip Service, a drama shot in Scotland, will not be re-commissioned and there will also be a two-year wait for the next series of the popular comedy Mrs Brown's Boys.
Kirsty Wark and Martha Kearney did not comment last night but one insider said: "It's a major change for the programme and people are not happy."
A spokeswoman said: "The BBC is committed to arts programmes and full details of any changes to The Review Show will be announced in due course."
BBC Scotland members of the National Union of Journalists (NUJ), which represents some of the staff at Pacific Quay, have decided to work to rule in protest against what they see as a lack of progress on redeploying staff, starting last night.
BBC Scotland aims to cut up to 120 posts from a workforce of 1250, after the licence fee freeze agreed with the UK Government in 2010. The cuts north of the Border are part of the wider savings strategy, called Delivering Quality First, which will see 2000 jobs go.
NUJ Scottish organiser Paul Holleran said: "A major concern is the loss of specialist reporters and correspondents. This will result in a serious dumbing down of output."
Michelle Stanistreet, NUJ general secretary said: "The BBC should withdraw the threat of compulsory redundancies in Scotland and take steps to redeploy staff at risk. Journalists will stand in solidarity with colleagues who risk losing their jobs and members have a clear mandate to take action to stop compulsory redundancies.
"Management must get round the table and explain why they are not using an agreed redeployment system – there is no excuse for not finding roles for the numbers involved."