To answer your question: Yes, Matt Cassel will be starting for the KC Chiefs next week.
Romeo Crennel opened up his postgame press conference following Sunday's game against the San Diego Chargers with a few remarks to the media and without being questioned he said Cassel would remain the Chiefs starting quarterback.
"I know there will be some questions about the quarterback. I'm staying with the quarterback and I stayed with him during the course of the game. I stayed with [Jamaal] Charles during the course of the game. And we're going to stay with him going forward at the moment."
I should highlight: "...at the moment." In reality, every position is "at the moment" because any coach would make any switch necessary to get a win.
But I think the Chiefs coaches are realistic -- Brady Quinn isn't obviously better than Cassel. There's the argument there for change for change's sake if things keep getting worse and maybe I can understand that.
Danny Parkins of 610 Sports asked Cassel during his postgame presser if Romeo had talked to him about making a change, and Cassel said no.
The turnovers have to stop. That's problem No. 1.