There has been lots of talk in recent days about a 'late surge' for Yvette Cooper, with some in Westminster even predicting she will pull off a surprise victory at the eleventh hour.
Of course this is technically possible. Cooper has had a good few weeks, while Corbyn has run into some real trouble. This year's general election should also make us all wary of following the consensus about what will happen in upcoming elections.
But if Cooper is about to shock the nation, it would fly in the face of all the available evidence.
On every measure, from the polling, to the CLP nominations, to campaign canvassing returns, to the sheer numbers of supporters Corbyn is turning out at his campaign events, he is well ahead.
Now it's true that the race could be much closer than it appears on all these measures, in which case there could be a reasonable chance that Cooper could win on second preferences. However, I have yet to find anybody outside of Cooper's own supporters who believes it is that close.
And I'm not just talking about Cooper's rivals. After all, briefings from rival political campaigns tend to bear as much resemblance to reality as a headline in the Pyongyang Times. But more interestingly, sources within Labour's London mayoral campaigns are also keen to stress that Corbyn is almost certain to win on first preferences alone.
One such source, sympathetic to Cooper, told me today that there was "absolutely no evidence" she was about to storm to victory.
"There's no doubt she's had a very good few weeks in purely Westminster terms, but how much effect will that have on the result when most people have already voted?" they said.
"I can't see it. They seem to be talking up the late surge of people signing up to vote as if they've all joined to stop Jeremy. It seems very unlikely."
Another source in the Labour mayoral campaigns described claims of a Cooper surge as "total nonsense," adding they were confident from their campaign calls with the selectorate that Jeremy would easily win on first preferences.
Tessa vs Sadiq
So with Corbyn almost certain of victory, what about the race to be Labour's London mayoral candidate?
Here the picture is much dimmer. There has been no official polling of the Labour selectorate, and only a handful of polls of the London public. What we do know is that there has been a massive influx of new members and supporters signing up to take part in the vote in London since May. We can also be fairly confident that these new members are overwhelmingly Corbyn-backers and therefore tend to be more left-leaning than the previous membership. We also know from the CLP nominations that Tessa Jowell's's pre-existing lead among the party establishment in London is by no means overwhelming.
Sadiq Khan's campaign remain incredibly bullish that their man is on course to win. Like Cooper they have had a good month, with endorsements from key figures in the party and the Labour-supporting press. Like Corbyn, Khan has benefited from the backing both of the unions and figures on the left like Ken Livingstone.
But as with the briefings of a last minute surge from Cooper's camp, the briefings from Khan's team should be taken with a massive pinch of salt. There are very good reasons to believe Khan could still beat Jowell, as there are similar reasons to believe Diane Abbott could do much better than has been predicted.
However, at this stage only a fool would say with any real confidence who will be announced as Labour's next mayoral candidate on Friday morning.