The Guardian reports today that the idea of having more repeats in BBC Four's schedule has been put forward in the corporation's Delivering Quality First efficiency drive.
Options still under consideration in the DQF process include the reduction of drama on BBC Four and sister channel BBC Three, along with the axing of BBC Two's daytime schedule.
BBC Three has often taken the brunt of criticism of the BBC's digital channels, but bosses at the corporation are understood to view the channel as more distinctive than BBC Four.
Management are concerned about an outcry if BBC Three is scaled back, after the channel has helped attract a key younger audience with popular shows such as Being Human and documentary Our War.
This means that more radical changes are now being considered at BBC Four, with the aim of turning the digital network into an "arts and archive" channel.
Despite receiving awards and acclaim for shows such as drama The Road to Coronation Street and comedy Getting On, some BBC executives have questioned the current remit of BBC Four.
In his statement of programme policy for BBC Four earlier in the year, the channel's controller Richard Klein tellingly did not mention drama or comedy in the opening summary.
Instead, Klein said that BBC Four would become "the gold card channel for arts and culture, approaching subject matter at a level of depth, detail and authority second to none".
A source told the newspaper: "The scope of BBC Four is under threat. The relationship between the four major channels is being looked at."
Final decisions in the DQF process are due to be agreed next month, and the BBC Trust has appointed Ernst & Young as advisers to scrutinise the financial impact of the proposals.
A Trust spokesman said: "We are not going to comment on speculation ahead of the Trust reaching final conclusions on Delivering Quality First."
A BBC spokesperson added: "We are not going to get drawn into a running commentary - no decisions have been taken and therefore these claims remain speculation. Any decisions coming out of the process would be subject to approval by the BBC Trust."
Also today, it emerged that the BBC is considering sharing TV coverage of the Olympic Games in 2016 with ITV or Channel 4 as part of its wide-ranging cost-cutting drive.