Cardinals coach Ken Whisenhunt told radio station KTAR on Monday that he hasn't made a final decision.
Leinart had three interceptions in the first half and completed just 4 of 12 passes for 24 yards. His passer rating was 2.8.
The Cardinals won the game 24-0.
The source said Leinart's training-camp performance has been uneven, and the Cardinals are concerned about his arm strength and consistency.
After the game, coach Ken Whisenhunt said Leinart was still in the running for the Cardinals' starting job.
"I know Matt's down because he didn't play as well as he would have liked," Whisenhunt said. "This competition, being pushed by Kurt, has made Matt tougher. It's one of the things you have to be as a quarterback."
ESPN's Chris Mortensen covers the NFL. Information from The Associated Press was used in this report.