Assuming we make the NCAA tournament, I don't think we're going to hear anything at earliest until we lose in it. Assuming we don't make it to the sweet 16, that means we'd hear something no earlier than between 3/20 and 3/23. And even then, we'd only hear something if our new coach is available, meaning either it's Brad/Jay Wright/Tony Bennett, etc. or our new coach's team has also already lost.
We can kinda start to figure out things by process of elimination once we lose and other teams start losing. Say we lose 3/20 and Iowa State, for example, gets upset on 3/22, but Drake makes the sweet 16. If we don't hear anything by that following week (3/23 on), we can probably assume Brad/Jay Wright/Tony Bennet/ and also Otz, are not the new coach, but perhaps McCollum is.