I feel like many people just throw out there possibilities for the sake of adding another thread to the discussion without much consideration of how many things work, but in particular: brand image. Within the current roster I see only two people handling the work: Hedi or Nicolas, with Hedi being much more fitting.
Chanel is, first of all, separate from all the big ones, it is its own. Nicolas is doing still well at LV, but I don't think his design language would translate too well into Chanel. He is very experimental, playful and strong on themes, but less so on personal touch. Also, bite me, but his tailoring is often slouchy and all around not good, it is just not his forte. Him and LV are a perfect match that should not be disturbed.
Hedi has the same principles as Karl, he is the best tailor currently available and he is way more of a personality. If they want a new Karl, he would be fit for the role, especially that he has enough years ahead of him to fulfil just that role. He also has a history with Dior, YSL and now Celine, it is a very similar trajectory with Karl and Balmain, Patou, Chloe, Fendi... They share string personalities and the desire for a lot of control, the difference is just that Karl is more playful and Hedi is razor-sharp.
Chanel should be put back on the map as The (!) luxury house, not what it is now with overexposure, strange direction, being outdated and mediocre at the same time, and losing its exclusivity. Chanel lacks refinement beyond its history and pricing.
Finally, I do not think that Galliano and many others are in the talks. Chanel is the core brand of French fashion, I do think that it being not owned by the conglomerate and being the "special" kid would nearly guarantee that it should be taken over by someone French, which John, Phoebe, Marc, and etc. are not.
LVMH can play with LV, Dior, Loewe, Celine, etc., because at the end of the day they are ones of many, existing as a symbiosis of companies under Bernard and co., Chanel is a different situation from all aspects: image, uniqueness, business operations. I think a lot of people do not take that part into account and approach it just as any other fashion brand.
Some choices are obvious and there is no need to overcomplicate things. The largest crowds of fashion people see that Hedi is the best option, despite liking and wanting other designers. I think they should go with the path of least resistance here. Strong control, quality and amazing tailoring is what people need right now of Chanel.
Jacquemus... I do get why that may be, but, personally, if that happens, even without seeing the clothes, just on the level of personality and experience of Jacquemus, Chanel would experience a huge drop in my eyes in terms of prestige. I'd, again, personally, stay away from Chanel if that happens.