The only viable option looks to be a short term one and so your choice is limited to the old, expensive lads, including Allardyce, Hiddink, van Gaal. Not convinced Anchelotti would consider us.
The reality is we haven't gone beyond the point of salvation and many managers know that. Some people on here are losing their shit and I can fully understand why but the fact remains we are a handful of points off the top 8, have a squad that whilst imbalanced is playing well below the standard the those players can play to (Martina aside); we have money available to invest without having to sell and ambition to go with it.
Whilst we are in a brutal run of form with confidence at its lowest, we are still a very appealing "project" to a lot of quality managers/coaches who also know we will pay them very well for the privilege. We need a quick fix in asap to galvanise the team, some impact signings from Walsh in Jan (I'm still prepared to give him time providing we give him autonomy too; only then will we know if his players are good enough) and then reassess candidates next summer when your chances of getting the one you want are vastly improved.
One of those candidates for me (and I'm fully prepared to get a hammering for this) would Brendan Rodgers.