I really don't want to give a concrete time because these things hit snags that can be due to external forces (I'm in the middle of a house purchase and the land registry searches are backed up to god knows where).
The aim is to get this done as quickly as possible, the Allams get their money and go, Ilicali comes in and can invest in January with a new manager. Somebody half joked that it might happen around the same time that the Allams took over (which IIRC was around mid to late December), but as far as I know it'll be done sooner than that. You'll start to see a lot more coming out in mid October, so if I was to give a time frame based on what I know (which admittedly isn't a lot) you're looking at early November, MAYBE late October if nothing goes wrong.
But like I said, these things are prone to drag. I think any worries of the Allams being here in the next transfer window can be quashed, but what damage is done to our league campaign in the meantime is down to McCann. He's basically fire fighting to keep us competitive, he knows he's going.