Rush believes Tom Hicks' remarkable admission he had spoken to Jurgen Klinsmann about taking over at Anfield is in danger of turning Rafa Benitez's reign into a Newcastle-style circus.
He told The Sun: "Now people are going to say the club is a laughing stock. In many ways, you can understand that because this is not the way Liverpool normally do things.
"The tradition of the club - and the very thing that has made them so hugely respected throughout the world - is to do everything in-house. Not out in the open like this.
"Look at Newcastle - we certainly don't want to get like that. That's just change for the sake of it. With Harry Redknapp turning them down, it's just going to drag on and on. That doesn't help anyone.
"But admitting that Klinsmann was approached is poor timing and puts a lot more pressure on Rafa.
"It's not just upsetting for Rafa but for the players and the fans as well. Everything seemed to be dying down a bit but now it's all been blown up again."
Rushie also rapped: "With respect to Klinsmann, how can he know more about European football than Rafa?
"As far as Europe is concerned, Benitez is the best.
"And as for English football, I think Rafa may know a bit more than Klinsmann!"
Typically, Hicks claims he and George Gillett are now "right behind" Benitez.
But as Rush said: "What else could they say?
"In fact, they shouldn't have said anything. Now many will look at Rafa as Dead Man Walking.
"Well, that's part and parcel of football these days. When Claudio Ranieri can get sacked for finishing second in the league and getting to the Champions League semi-final, anything can happen.
"And it has. We're only in January and eight Premier League managers have gone. Yes, expectations are high and owners want instant results but some of the sackings have been ridiculous.
"Sammy Lee didn't get a chance, nor did Sam Allardyce. But Liverpool must not go down the same path.
"And they certainly must not make it all so public.