Pressure has been growing on Kelly due to his side's performances this season following their 45-17 defeat to the Detroit Lions, their third loss on the spin.
Reports suggested that Kelly was interested in the vacancy at USC and had held talks on Friday, but the 52-year-old has dismissed the rumours as untrue.
"No, I've never spoken to anybody from USC," Kelly told reporters. "I've never emailed anybody from USC. I haven't gotten a phone call from anybody from USC, never had any contact with anybody from Southern California.
"I've never been looking at college jobs, but again, I can't control what's written. I was never looking at the Florida job last year. I said the same thing when they hired Jim McElwain - they did a great job, Jim's done a great job there."
USC hired Clay Helton as their new head coach on Monday following his spell in temporary charge.