Filling both these rather distinct roles at once is a tall order - especially at the moment. One job looks like the biggest toy box in the western world (OK, in reality it probably isn't - but who wouldn't love to dream up their perfect Proms season?). The other...doesn't; on the one hand, whoever runs Radio 3 will probably have to wield a sharp-edged axe, but on the other, the recently appointed director general, Tony Hall, is the most sympathetic to the arts in many a long year. Who could be in the frame to take over?
In the spirit of fantasy football - for none of us have much idea which way things might go - here is my personal shortlist for the headhunters' reference.
The director of the Proms needs the experience, the knowledge, the contacts, the drive, the ambition, the personality and the thickness of skin to reach for the stars. It is high time, of course, that the Proms was run by a woman. It's been run by a man for over 100 years. Radio 3, of course, has never been run by a woman either. Chances are probably limited, given the male weighting within the station and its listeners, but you never know; stuff could yet be swayed. Here is a 50-50 selection in no particular order, plus a little thinking outside the box. Some of these names have been bandied about a lot; others haven't, but perhaps should be.
GILLIAN MOORE. The Southbank's head of music has a simply staggering breadth of knowledge about the classical repertoire, not least contemporary music - and commissioning the latter is a vital part of the Proms role. She's also stupendously creative in programme planning. Witness last year's The Rest is Noise.
ALAN RUSBRIDGER. The editor of The Guardian is a passionate music lover and clearly has the cool head, steady hand and strength of personality to carry off the joint post and all it entails. After dealing concurrently with Snowden and learning the Chopin G minor Ballade, he might find it a tempting piece of cake.
JOHN GILHOOLY. Running the Wigmore Hall is something that nobody would want to stop doing - unless they wished to be let off the leash with a bigger place and programmes to match. He has an impeccable track record as chief exec and artistic director of the Wiggy and head of the Royal Philharmonic Society. (PS - John, when you get this appointment, please can I have the Wigmore job? Thanxbijx.)
KATHRYN MCDOWELL. As CEO of the LSO she is accustomed to dealing with Gergiev, so probably most other jobs will seem a picnic. She's maintained the orchestra's position at the top of the UK's orchestral tree while keeping discretion, valour and a level head.
TOM SERVICE. The critic and broadcaster is virtually a walking musical encyclopaedia - and is a brilliant communicator, too. His soundness, enthusiasm and conviction would be invaluable assets in the role. Nicholas Kenyon went to this job from being a critic and broadcaster, so precedent exists.
FIONA MADDOCKS. The Observer's music critic, she is a former editor of BBC Music Magazine and along with the necessary breadth of knowledge she has managerial experience, a razor-sharp brain and a scrupulous attitude towards fairness and balance.
...Anyway, I know who I think should get the job, but we are not yet off to the bookies to place bets.