Hm...potential GMs (all of the ones I can think of that would make sense):
Shane or Stephanie McMahon
Jerry "The King" Lawler
Stone Cold Steve Austin
Eric Bischoff (doesn't even appear remotely possible at this point)
Edge being GM would be crazy, kind of like when HBK was made into commissioner
Now after I got word that Armando Alejandro Estrada is returning, he is another former GM who makes a good candidate
Or maybe...JOHN CENA. (I dislike his character and his Hulkamania or "Super Cena" status, but he's top dawg, still...somehow.)
Consider this (and for the same reasons as Edge, kind of): He has been working injured for a LONG time. The WWE will want to keep his face on their programming, so they could make him GM and get promos from him, without any wrestling.
I believe that may be why they did that with Austin.
BUT WHAT IF (Most unlikely)...:
BROCK LESNAR!!!!! I don't know how on Earth this would work, but that would probably be one of the largest swerves in recent years
TNA gets sold, Dixie pulls a Bischoff...and joins WWE television as GM
or it could be Jarrett or Kurt Angle...lol don't know how those would pan out, except that Double J was sort of a commissioner on TNA and Angle, who has been hurt for awhile, and is only getting much older at this stage, has been in the GM role.
That's everyone I can think of that makes sense and remains somewhat relevant.