The proposed exit was announced as part of a £150 million worth of savings announced by the BBC's Director General Tony Hall this morning.
BBC Red Button consists of two distinct services; a digital text service that replaced Ceefax, lifting content from BBC News and Sport websites, plus a video service covering major events such as Wimbledon and Glastonbury as well as providing extra footage from BBC TV shows such as Springwatch.
The phased exit is linked to cuts in the overall cost of distributing BBC TV and radio services, which could also see AM radio services being axed.
In the move that would see the broadcast Red Button streams close, the BBC said it wanted to focus on its connected TV offerings available on TV platforms such as YouView and on Smart TVs, currently under the banner of "Red Button+" and BBC News and Sport Apps, as well providing extra content via BBC iPlayer.
Once a multi-screen service, following the 2012 London Olympics, the BBC reduced the linear BBC Red Button video service to one full-time stream on all TV platforms, with extra pop-up streams appearing during special events such as the Winter Olympics, Commonwealth Games and Glastonbury. Freeview's Red Button service had been cut in late 2009 to one stream to make capacity available for HD channels.
Since 2013, the BBC has been developing its connected Red Button service, which sees online content from BBC News, BBC Sport and the iPlayer launching via the red button, instead of the original version of the service.
Cutting the remaining Red Button video stream service on Freeview would come at a time when broadcasters are considering plans to migrate their terrestrial offerings to the newer DVB-T2 standard at the end of the decade, which is expected to result in all BBC TV channels being distributed in HD. It would, however provide an opportunity to end the current timesharing arrangement in Scotland, where several BBC radio stations close down every evening to make way for BBC Alba, due to a lack of broadcast capacity in Scotland to fully accommodate the Gaelic channel.