KEVIN CORKE (FOX NEWS CORRESPONDENT): A source did tell me last night that she wouldn't be surprised if the president, Bill, stayed in-house for a possible replacement for chief of staff. Now, that's interesting because that would mean, possibly, our old colleague, [White House Communications Director and former Fox News co-president] Bill Shine could be a name to keep in mind, but we haven't heard that yet either from the president. 

Previously:

Fox News runs the government

Report: White House is waiving ethics rules so former Fox co-President Bill Shine can talk to the network

Both of Roger Ailes' replacements have now been accused of participating in Fox News' culture of sexual harassment

How Bill Shine has been implicated in Fox News' ongoing legal disasters