I have thought about that a lot actually.
First, Harris has a list of guys he is at least interested in talking to by now. I think putting that list together was part of bringing Shen in when he did (unless he is thinking Shen might be his new GM? hmmmm). I figure that there has to be some back-channel communication going on with agents for prospective GM candidates on that list. By now, Harris should know who is interested and who isn't, and candidates know they have to be prepared to talk.
If I have aspirations of being a GM one day, I keep a living list in my back pocket of guys I think I want to work with - both in my front office and on my sideline. This list is important because it is likely figure large any interview process with an Owner looking to turn over the operations of their organization to me. I'm also watching tape of any team interested in me every night after the wife and kids go to bed to prep for formal interviews.
Many of the top coaching candidates are on playoff teams so there is only so much that can be done until their season is over anyway which means we have a bit of breathing room on the GM front.
Arizona did the GM/HC double change last year. They announced their GM hire on Jan 16th (Monte Ossenfort, former Dir of Player Personnel with Tennessee) and their new Head Coach on Feb 14th (Jonathan Gannon, former Eagles DC). The regular season ended on Sunday, Jan 8th.
Here is last year's
official timeline, per NFL rules, on interviews for coaching candidates. I haven't found an official timeline for front office personnel but I would be shocked if there isn't a significant amount of informal communication going on right now.
The Rooney Rule is also in effect for both GM and HC positions - minimum 2 minority or women candidates for both positions.