The comedian quit the corporation in 2008 after he and Jonathan Ross caused controversy with prank phone calls to actor Andrew Sachs.
Brand is now developing a film about addiction for the broadcaster, which would mark the first time he has hosted a BBC programme since the Sachsgate scandal.
He is thought to have offered to appear in the documentary for free as a peace offering to the BBC, The Guardian reports.
Both parties are still in discussions regarding the show, but it would explore the issue of addiction in a similar way to how Stephen Fry looked at depression for BBC Two back in 2006.
A BBC spokesman said: "We are working with Russell on a programme about addiction in the UK but it's currently only in its early stages."
Brand has often discussed his own drug abuse and last year posted a passionate tribute to Amy Winehouse following her death, in which he called for a rethink on the way addicts are treated.
"We need to review the way society treats addicts... we need to look at the way our government funds rehabilitation. It is cheaper to rehabilitate an addict than to send them to prison, so criminalisation doesn't even make economic sense," he said.
He has co-hosted a sports show with Noel Gallagher on TalkSport in 2009 and appeared as a guest on Dermot O'Leary's BBC Radio 2 show in 2010 since leaving the BBC.
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