In total, more than 36,000 people have now joined a Facebook group Save BBC 6 Music.
On its homepage, the group says, "The BBC Trust is about to publish a review into the performance of both 6 Music and Radio 2. There are rumours that the station, which has 620,000 weekly listeners and costs £7 million a year to run, could be closed in a meaningless sacrifice to politicians demanding BBC savings and a limit on the corporation's digital ambitions.
"The Trust could argue that 6's audience reach doesn't justify its expense and that its core audience be served in the margins of a tightened-up Radio 2."
However, 6 Music was one on few bright spots for digital station in recent Rajar figures: it had 695,000 listeners, up 11.4% on the previous quarter and 12.3% year on year, in a period in which most digital stations saw their audiences fall.
The BBC's statement does not entirely rebut the rumours, pointing out instead that there is a wider BBC strategy review currently taking place and no decisions will be made before then.
"All services are being reviewed at the moment as a part of the BBC-wide Strategy Review and [Director General] Mark Thompson has said that the review will be announced at the end of February/beginning of March," the BBC statement explains.