For a job of this importance and stature, the short list is questionable. Not just who is on it but each brings a different level of experience, a different cultural and footballing background and it seems to me none truly fit the urgent requirements.
We have short term needs (win matches to stay up and make the most of the squad already in place as that is what they will be working with): mid term needs (identify and shift deadwood, replace with better and hungrier players, rebuild clubs internal and external relationships, help develop and implement football strategy) and longer term ambitions (compete regularly at the top level and win things as well play attractive and effective football).
The three being interviewed don't make me think they can do 2 and 3 at all and point 1 might make Lampard (always been at a successful environment including Derby who paid for theirs) and Pereira (will need time to integrate and time is not what we have) none starters for me.
I'd look at either Ferguson till season's end or someone like Nigel Pearson only till season's end. Use the time to interview longer term and a more diverse list of managers but who all have a consistent strategy. 
I'd look at Potter, Steve Cooper, Rooney, Marco Rose, Diego Martinez and (I know) Xabi Alonso. All "technical coaches" who play progressive football. All would need a strong Director of Football and we should use this time to build this 
Thanks for reading.