It’s the biggest job in British theatre – and the biggest question is always who the successor might be to the current incumbent: namely, the artistic directorship of the National Theatre. And Nick Hytner, who in four months time will have been at the National for ten years, is going to be a particularly tough act to follow.

He’s introduced bold new innovations, from pricing policy with the Travelex £10 season (now £12) to initiating the NT’s internal and exterior transformations that are now underway. And he’s also become the best, and loudest, spokesperson for the theatre.

Not that he’s announced, anyway, that he’s going anytime soon. But I posed the question casually on Twitter on Sunday, after reading an interview with Michael Grandage in that day’s Culture section of the Sunday Times, in which he categorically stated:

I’ve done my running of buildings. Now I want to ­concentrate on a company that can do anything, to keep me moving forward and out of a comfort zone… I will not ever apply to the National or any other building.

He was, at one point, widely being tipped as the likely successor to Hytner, for whom he once worked as an actor at the beginning of (both of) their careers; but now that he says he won’t do be applying, who will?

My own immediate Twitter shortlist comprised Dominic Cooke, soon to depart from the Royal Court; Tom Morris, who left the National where he was an associate to take over Bristol Old Vic, but could return having gained the experience of being in charge of not only revitalizing a troubled building but also overseeing its (part) refurbishment; and of course Rupert Goold, who turns up on every list of every job these days (and I strongly suspect may yet grab the Almeida after Michael Attenborough’s departure).

But I also proposed another in-house candidate: Nick Starr, currently Hytner’s trusty lieutenant as executive director, who has managed to grow the theatre’s commercial arms to the point where it no longer needs to farm out transfers to the West End and beyond, but is self-producing them (with War Horse and One Man Two Guvnors currently there, to be followed in March by The Curious Incident of the Dog in the Night-time), and has also recently set up a New York office to supervise the NT’s North American operations.

He is already, in a very real sense, running the place; and an administrative artistic director, freed up of the need to spend time in rehearsal rooms, is not an altogether bad idea. It is what Jenny Topper did at Hampstead, and Rachel Tackley does at English Touring Theatre. On the other hand, perhaps when Hytner goes, Starr will have had enough, too – maybe they’ll both follow in the footsteps of Grandage and his executive director James Bierman to set up a joint commercial venture of their own.

Then there’s Jonathan Church, who has made such a success of Chichester (as he did with Salisbury and Birmingham before that), but he is yet to direct at the National, and is widely thought to be a far better producer than a director. One more candidate I put forward was Rufus Norris, a director with a strong NT track record including last year’s London Road, who is much beloved of actors who work with him.

Of course, if we’re also looking through the names of existing NT house directors, Marianne Elliott, Katie Mitchell and Thea Sharrock must inevitably be named, but all have limited experience at the helm of buildings. Elliott was once part of the team at Manchester’s Royal Exchange, while Sharrock has run the fringe Southwark Playhouse and Gate. Both, of course, have proved that they can marshal a crowd, with respectively War Horse and The Bodyguard. Howard Davies, the NT’s best secret weapon, might be another name but he has shown no desire to run a venue before.

Candidates for the future might include Laurie Sansom (soon to take over at National Theatre of Scotland) and Indhu Rubasingham (newly installed at the Tricycle), depending on the successes of those ventures.

Or perhaps it’s time to think (further) outside the box; how about an actor? Kenneth Branagh was being mentioned for the RSC; how about Simon Russell Beale and Alex Jennings teaming up for the National?