They didn't necessarily look, I think it was discussed with Jose about him working with a DoF and he disliked the idea. Now that's not to say they didn't have some candidates in mind. Having a candidate in mind is different to having interviewed them and feeling they are right for the job.
Weather any of us like it or not, it is indeed a time consuming process. As mentioned our previous manager was against the idea from all reports, that manager is now gone. Candidate list drawn up, interviews / discussions to take place, offers to be made and finally accepted.
It involves a lengthy process, if you doubt me feel free to see how many years it took Man City to roll out their project for Pep, They acquired staff from Barca over 3-4 seasons and the final piece of course was Pep himself.
Likewise Liverpool's project with Klopp has taken how many years? That number again? He's on his 4th season and reaping the rewards from a stable backroom and scouting network.
Another example is our own Sir Alex, Hired in Nov 86 and didn't win a trophy until 4 season's later, a league took 6 years.
So no, two months is not enough, unless you think this is football manager or the like.