The source said Arizona State's explanation was that "it took too long" and the school president was moving on.
"We had accepted the deal," the source said. "I've never seen anything like this."
One source said negative reaction from fans and boosters to the selection of Jones prompted the reversal. Arizona State has now negotiated with and ended negotiations with two candidates, including Houston's Kevin Sumlin.
Earlier Wednesday, sources said the school was preparing to announce Jones as the Sun Devils' next coach.
Arizona State dismissed Dennis Erickson a week ago after five seasons.
Jones, who spent the last four seasons at SMU, was formerly a coach at Hawaii and for the NFL's San Diego Chargers and Atlanta Falcons.
Jones spent nine seasons at Hawaii, leading the Warriors to the Sugar Bowl in 2007.
Jones has led the Mustangs, a program that was still recovering from the NCAA "death penalty" of the 1980s, to three bowl games in four seasons.
This season, SMU went 7-5 overall and 5-3 in Conference USA. The Mustangs will play Pittsburgh in the BBVA Compass bowl Jan. 7.
Information from ESPN.com Pac-12 writer Ted Miller and ESPN college football reporter Joe Schad was used in this report.
NOTE: CHECK OUT THE MESSAGE BOARDS ON THIS. THE FANS ARE NEARLY UNANOMOUS ON THIS THAT JONES WAS THE WRONG CHOICE.