Today, Trust chairman Sir Michael Lyons laid out initial conclusions on BBC director general Mark Thompson's strategy review for the corporation, which included plans to close 6 Music and its sister station The Asian Network.
The move to axe 6 Music has led to widespread protests, including strong views expressed by listeners, musicians, industry bodies and even politicians.
In a statement, Lyons said that Thompson's strategy review has not made a sufficient enough case to support the closure of 6 Music.
The chairman said that Thompson should now conduct a wider consultation on the BBC's "overarching strategy" for digital radio.
He also said that the Trust would "consider" a proposal for the closure of the Asian Network, but that must factor in how the station's audience will be served elsewhere.
"The Trust concludes that, as things stand, the case has not been made for the closure of 6 Music," said Lyons.
"The Executive should draw up an overarching strategy for digital radio. If the director general wanted to propose a different shape for the BBC's music radio stations as part of a new strategy, the Trust would consider it.
"The Trust would consider a formal proposal for the closure of the Asian Network, although this must include a proposition for meeting the needs of the station's audience in different ways."