We don't know but perhaps we were trying to keep the Klopp news quiet (I assume the players didn't know) and leaked it when we did precisely so we could start sounding out candidates (including Edwards).
My theory is he told them in November. Though they give him until January to reconsider before notfying the squad, and thats what drove the announcement timing. Once he confirmed in Jan he wasn't for turning on the decision and once Gordon and co had offered whatever they thought would keep him (player funds, salary increase, greater assistance, sabbatical etc). I'm sure they would have insisted he rested on the decision for a reasonable period, given the magnitude of it.
They would have began shortlisting on paper from Nov, however no agent or candidate would have been approached until he publicly announced it, otherwise at that point it would have got out in an unmanaged way, causing all sorts of problems whether sporting, PR or from a club business perspective. That was why it was important to make it public so It would be known the vacancy will exist, manage the delivery of sad news plus crucially - at that point agents could be contacted without the fear this news would have leaked.
I'm under no doubt that the candidates have been contacted, and they will have indicated thier interest or not at the very least by now, perhaps even as far as a verbal agreement to join, subject to negotiations with clubs to release them and contracts being agreed.
Knowing how shrewd FSG are, it feels more probable than not to me that a select few know who the next manager will be, though until the season finisheses, legal admistraitive matters dealt with , they couldn't, even if they wanted to, announce it until after the end of the season, as thats the earliest point when actual contracts can be terminated, compensation paid and new contracts signed.
