The plans will be announced today but many of its shows, aimed at a younger audience than more mainstream channels, are expected to be transferred directly to the iPlayer.
Director-general Tony Hall, in a speech last week to the Oxford Media Convention, said the BBC needed to make more cuts as part of its bid to save £100 million but he ruled out "salami slicing" from every department and said he wanted to "focus on what we do best".
That sparked speculation either BBC4 or BBC3 would be axed, and corporation bosses believe BBC3's younger audience would be more likely to access content online and that any move to cut the more high-brow BBC4 would face criticism.
An online campaign opposing the BBC3 move has already been launched and has been backed by some of the stars who launched their careers on the channel.
Comedy star Jack Whitehall, who wrote and starred in Bad Education on the channel, said: "I really hope reports the BBC may kill BBC3 are just rumours. Their support of new comedy in particular is vital."
Matt Lucas, who appeared in Little Britain, said closure would be "really bad for new comedy".
The station's target audience is 16-34-year-olds and hit shows have included Torchwood, Gavin and Stacey and comedy cartoon series Family Guy.
The BBC spent £89.m on content on the channel in 2012/13, more than the £50m spent on content on BBC4, but its costs per user hour were 6.6 pence, making it cheaper than both BBC2 and BBC4 by that measure.
Moving BBC3's content to the iPlayer would fit with Mr Hall's previously announced plan to extend the licence fee to cover people watching BBC programmes online. At the moment the £145.50 fee is payable by everyone in the UK who watches or records BBC programmes when they are shown - meaning the on-demand iPlayer is not included.
However, any proposal to close BBC3 or move it wholesale to the iPlayer would have to be approved by the BBC Trust, the corporation's governing body.
The possible closure echoes the situation in 2010 when the BBC proposed pulling the plug on two of its digital radio services, 6 Music and Asian Network, prompting a backlash from listeners, celebrities and even MPs.
The outlined cuts were as a result of a strategy review that had the aim of shaving millions of pounds from the BBC budget. Figures such as David Bowie, Coldplay and record industry executives gave their support to 6 Music, which at the time cost about £9m a year to run.
But the publicity surrounding the possible demise had the effect of driving up listening and awareness of the station, which at the time was something of a niche concern.
The BBC Trust eventually rejected the closure of 6 Music and it has gone on to see its audience treble, with just 600,000 listening before the report, but 1.96 million now tune in, according to latest figures. Plans to close the Asian Network were also eventually dropped.
Mr Hall told Radio 4's World At One last October he would not consider closing a channel to save money. Speaking then, he said: "No I wouldn't consider closing a channel. I think people know the public feel very strongly about all the services the BBC does. No, we have to find other ways of prioritising."
But last week he said: "Our view is there is room for modernisation so the fee applies to the consumption of BBC TV programmes, whether live on BBC One or on-demand via the iPlayer."
The last BBC annual report said BBC3 reached 29% of its target audience of 16-34 year olds each week and "continued to deliver high quality" programmes.