Little said the Bombers, who are in negotiations with the AFL over their penalty, will attend a scheduled AFL Commission hearing on Monday.
He is confident the League and the club are close to reaching a "middle ground" on penalties which both parties can accept, although he said he could not guarantee it would be achieved before the finals.
The sanctions are likely to include the Bombers being stripped of premiership points and their finals berth, and being fined heavily, as well as a ban for Hird.
But Little would not confirm any of those details, saying he did not want to pre-empt the outcome.
Asked if Saturday night's game against Carlton could be Hird's last in charge of the club, Little said he did not believe so.
"I'm certain that that's not being requested at this stage, so I would say no to that," Little told the Seven Network pre-match.
He said the Bombers would want Hird back in charge if he had to serve a 12-month ban.
"Absolutely and that would be our preference," Little said.
He said he did not want to answer on Hird's behalf as to what would be an appropriate sanction for the coach.
Little also confirmed the AFL had given the club the option of accepting a penalty on their own behalf, while leaving Hird and club doctor Bruce Reid to battle the League separately, if they chose to.
"At this stage all I can say to you is it is a package (being negotiated between the Bombers and the AFL) other than the option that's been given for James or Bruce Reid to opt out of that should they wish to," Little said.
"But we're trying very hard to get the package agreed."
Little said he hoped Hird would get his time to tell his side of the story.
"James is very remorseful. I've spoken to him, he's spoken to the parents, we see that as a very private area of him admitting remorse," Little said.
"James is remorseful and he's looking for an opportunity to actually express that and at this point in time it's not going to be a five-second message out the front of his house."
Little said the prospect of Essendon participating in this year's finals series was being negotiated with the AFL.
"At this stage it's part of what I'm working through with the AFL and it's certainly on the table, both from the AFL's point of view and our point of view," Little said.
"It will become clearer when we reach agreement with the AFL."
Little said he was "personally disappointed" with the collective response of the 17 other club presidents and chairmen who attended a meeting at AFL House on Thursday to be updated on the situation.
They unanimously expressed their support in the AFL's management and commission.
"I have to say it was my first time that I've had an opportunity to speak with the other clubs," he said.
"I was somewhat disappointed that the other clubs offered a lot of support and then put out a notice that they were strongly behind the AFL, however that was always their prerogative."
One of those presidents was Carlton's Stephen Kernahan who, at the Blues' pre-game function, wished the Bombers well, and outlined his hopes for a swift resolution to the saga.
He compared Essendon's situation with the punishments handed down to his own club in 2002, when it received heavy draft penalties for salary cap breaches.
"Your words of yesterday, you said you were trying to get a quick end to this, and I've just spoken to you now, and you're trying to do that over the next 48 hours," Kernahan said to Little.
"But it's easy for us to say – it's been a really tough time for the club.
"You've got a lot of very good football people; let's not lose sight of that fact.
"They haven't killed anyone. Nothing drastic has happened.
"So I wish you all the best, and I say that sincerely. It's a tough game, football.
"Carlton went through it 10 years ago, and that was a tough time, and we're still trying to come out of that.
"There's great respect [at Carlton] for the good football people [at Essendon], so good luck."
