Speaking at the MediaGuardian's Radio Reborn conference in London today, Davie told delegates that "continuing current purchase trends would not lead to radio switchover in our lifetime".
Davie says there need to be better, cheaper DAB radios for people to buy. "Freeview happened because you could pick up a £20 set-top box in Tesco and away you go."
He has called for "a real and secure road map" to digital radio, but warned there are "huge risks" ahead.
With this in mind, the BBC and commercial radio are to join forces to set up a cross-industry Radio Council to secure the medium's future, according to MediaGuardian.
One of the Radio Council's first aims is to create a cross-platform radio player and electronic programme guide (EPG) for BBC and commercial stations, called Radio+. If it gets the go-ahead, it could be launched by the end of this year.