In 18 days a meeting will take place which will go a huge way towards shaping the relationship between the Celtic squad and the man who is on the brink of being appointed as their manager.
They will have read far more about Deila by then, seen him on television and spoken to folk around the club who have met him. But it is on June 24, on the first day of pre-season training, that they will encounter him themselves and start to make up their own minds.
Footballers can be strange and unpredictable. They can think as a pack. They want their managers to be good so that they secure more trophies, more win bonuses, more Champions League football, more spin-off benefits in their careers. And they want all that without the boss being too much of a hard case who is on their back all the time.
But packs are also quick to sense weakness in a newcomer, especially a new leader. At 38, Deila is the youngest Celtic manager since John Barnes (a few months older than Neil Lennon was when he got the job) and does not carry the authority which comes naturally from being a couple of decades older than the players. Nor does he boast a playing background which will impress any of the players he is about to inherit.
He is not going to be coming off best in any "show us your medals" challenges with Celtic men who have won titles and cups and beaten Barcelona in the Champions League.
It may surprise Deila that he might also have to face some mild inverted snobbery about the fact "qualified teacher" appears on his curriculum vitae. British football has long held a suspicion towards men whose coaching credentials are intertwined with a formal background in education, as Andy Roxburgh and Craig Brown can testify. It is a baseless suspicion given that Rinus Michels, Ottmar Hitzfeld and Jose Mourinho have similar origins, but it is the sort of thing which is cast up and held against a manager who does not make a solid first impression.
At least Deila, like all former teachers, has one thing in his armoury which should help him in dealing with any questioning of his credentials: intelligence.
Brains alone will not help him - Barnes and Tony Mowbray were no dunces - but what Deila will have to show from the start is charm, personality, wit, discipline, football knowledge and insight.
First impressions count and no matter how impressive Deila's record at Stromsgodset has been it is not Billy McNeill, Martin O'Neill or Henrik Larsson walking into the room. Those Celtic players need to come away on June 24 and, once Deila is out of earshot, they need to say to each other that he came across well, that they liked this bit or that, that it will be interesting to see what does the next day. And over the following weeks they need to warm to him and his methods.
As long as influential figures in the dressing room - Scott Brown, Kris Commons, Charlie Mulgrew - buy into him, the rest will follow. Deila does not need to be liked - many of the best managers would not win any popularity tests - but he has to immediately come across as a man of substance.
Even a manager of real experience and quality, David Moyes, struggled and eventually failed when he inherited a group of players at Manchester United who seemed to believe they should have better than him. The key issue is respect.
Celtic are privately hopeful that their supporters, and the media, will give Deila time but what is essential is that the players are receptive towards him in the crucial first few weeks and months in which opinions will form, shaped by results in the one, two or three Champions League qualifying rounds and/or how they get on in the group stage or in the Europa League.
In some ways his timing is unfortunate: two of Celtic's key men, Fraser Forster and Virgil van Dijk, could be plucked from him within weeks. Instantly he will face a baptism of fire in the six-game season-within-a-season Celtic must negotiate to qualify for the Champions League group. But in other senses any confident and ambitious younger manager could only jump at the window of opportunity to take on a team which has just won its league by 29 points while its only comparable rival remains in self-inflicted exile for another season.
What only the coming weeks and months can show is whether Deila carries the element of luck essential to all successful managers.
His reputation could be directly affected by matters outwith his control. He can have no input to who Celtic face when the Champions League qualifying round draws are made on June 23 and, assuming they progress, July 18 and August 8.
If he is lucky, they will be paired with favourable opponents. If they land a nasty draw he will be right up against it right away.
With regards to injuries and transfer activity he needs a kind following wind, too. Barnes' Celtic career was only 14 games old when Larsson suffered a double leg break which finished his season.
If he is fortunate Deila will not lose anyone crucial. If he is even luckier, no irresistible bids will come in to Celtic for Forster, Van Dijk or anyone else he would wish to keep.
Every new appointment "feels right" to a board of directors when it's made. Martin O'Neill, Gordon Strachan and Lennon felt right to Celtic and so, at the time, did Barnes and Mowbray. Right now Deila feels right to them too, and the response from most fans has been a sort of measured, intrigued, willingness to give him a chance.
A general goodwill is there, and when he meets his players it will be up to him to start building on that.