They originally toyed with the idea of the likes of Marjorie Scardino and Patience Wheatcroft, but I have been told this lunchtime by a senior government source that Sebastian Coe is now the clear front runner to be the next Chair of the BBC Trust.
There are a few hurdles left to clear and obstacles that can be placed in his way, but I am told he is interested and that he enjoys the firm support of the Prime Minister and the Chancellor. Given that this is basically a Number Ten appointment, that should more or less settle it.
The truth is that, whilst the Prime Minister and the Chancellor quite like the new Head of BBC News and Current Affairs James Harding (former Editor of The Times), they remain suspicious of the BBC generally, both in terms of inherent bias and alleged profligacy. So this appointment was always going to be someone they wholeheartedly approved of, which basically means a politician from the Tory family.
Given that, Sebastian Coe is a rather clever choice. The Olympics was an undeniable triumph and the BBC had a significant share in that. It is, you might say, an obvious marriage.
It would also place Lord Coe in pole position to stand as Mayor of London when Boris steps down, should he want to make the switch.