Blue Peter could disappear from its BBC1 home after more than 50 years under proposals being discussed.
The show, part of the bedrock of the TV landscape for successive generations, is the longest-running children's show in the world.
But senior BBC staff have talked about moving it from the flagship channel to digital station CBBC.
The idea is said to have been floated as part of the Delivering Quality First initiative which is looking at efficiency savings to cut budget costs.
Blue Peter has had a strong presence on CBBC for many years, airing repeats and spin-off shows.
It has continued to have its main home on BBC1 where it is broadcast twice a week at 4.30pm, although the audience is higher for its digital screenings as youngsters increasingly turn to dedicated channels. Station bosses cut the number of editions of Blue Peter from three to two in 2007.
Television industry magazine Broadcast reports that the idea has been raised to end the "children's block" of afternoon shows for younger viewers on BBC1 and instead show them exclusively on digital channels CBBC and Cbeebies.
It is one of a number of radical ideas which have been floated to reorganise viewing in a bid to refocus money under the Delivering Quality First initiative. They have included dropping overnight programmes on BBC1 and dropping daytime shows on BBC2 in favour of rolling news.
A BBC spokeswoman said: "It is important to stress that this is only one of many DQF proposals and that there are no immediate plans to remove children's content from the BBC's terrestrial channels."
BBC research has shown that the number of youngsters in the CBBC target age range of six to 12 who only watch the channel's content on BBC1 is declining.Reuse content