It follows the success of shows including Normal People, which helped the corporation reach the crucial target of younger viewers, the PA news agency understands.
The youth-focused channel went digital-only in 2016 in a move that saved the broadcaster a reported £30 million, but following a strong showing for BBC Three during lockdown, the corporation expects to double the amount it spends on commissions for the channel over the next two years.
Normal People, its adaptation of Sally Rooney's acclaimed novel, arrived on iPlayer in April and has so far had 38 million requests to view it, according to the BBC.
Ahead of publishing its annual plan on Wednesday, it is understood the BBC believes it has recaptured a young audience in “dramatic fashion” during lockdown.
Amid cost-cutting measures of about £125 million enforced by the coronavirus pandemic, a source said the corporation will have to trim budgets in some areas to invest in others, and BBC Three “would be a key beneficiary of that”.
However, following reports BBC Four was in danger of closing, a source insisted the move is “not about playing off” the two channels, saying the corporation has “no plans” to diminish its arts portfolio.
The source said no final decisions have been taken and options will be considered as viewing habits develop during the Covid-19 crisis.
It is understood iPlayer, which now allows viewers to watch many shows in a window of up to a year, has recorded more than one billion programme requests during lockdown.
A BBC source said: “Clearly no organisation from the smallest shop to the largest multinational won't be changed by this pandemic.
“It will have financial implications for the BBC, but that doesn't mean we can't make choices. BBC Three has become the home to some of our biggest shows.
“We need to back that success, so within an environment where we are making difficult cuts, this is one of a limited number of areas, where we will seek to invest.
“Who wouldn't want more Fleabags, Killing Eves, This Country or Normal People?”
Recapturing a younger audience is seen as a key task for the new director-general. Lord Hall announced his decision to step down in January after seven years in the post.
Last year Ofcom warned the BBC is at risk of losing “a generation of viewers” if it cannot engage a younger audience.
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