Jauron was the second coach to interview, following Bills special-teams coach Bobby April on Friday.
Other potential candidates appear to be former Packers coach Mike Sherman, Saints coach Jim Haslett, and Baltimore Ravens offensive coordinator Jim Fassel.
Rivera is expected have a second interview with the Rams as soon as today and is competing with Dolphins offensive coordinator Scott Linehan and Chargers offensive coordinator Cam Cameron.
At this point, Linehan is considered the favorite to replace Mike Martz.
If Rivera is offered a head coaching position, there is a plan in place to find his replacement. Tampa Bay defensive line coach Rod Marinelli was initially Lovie Smith's first choice when he was hired, but the Buccaneers would not grant the Bears permission for the interview.
Marinelli is a candidate for the Lions head coaching vacancy. If he fails to land the job in Detroit, Marinelli would be on the Bears short list of candidates to replace Rivera.
San Francisco linebackers coach Mike Singletary has been eliminated as a candidate with the Lions.
No Backfield Controversy
Even though Cedric Benson's rookie year could be classified as disappointing, the Bears didn't take the running back with the fourth overall pick to have him sit on the bench.
A holdout obviously had an impact on his season, as did a knee sprain that sidelined him for six games. Next year, the Bears expect to see the Benson that ran for more than 5,500 yards during his four years at Texas.
However, nothing will be given to Benson. He will have the chance to carry the ball more frequently, but the starting job is Thomas Jones' to lose after he became just the second running back in franchise history to go over 1,300 yards in a season.
"Thomas had a great year," said Coach Lovie Smith. "As we talk about all the positions we have a starting rotation but it's just that. Every position we have there's a starting rotation. Thomas is definitely No. 1 in our starting rotation but all guys know that they have to perform a certain way to stay there."
Bernard Berrian handled the punt return duties late in the year. He averaged 8.6 yards on 8 attempts and had no problems catching the ball, something that couldn't be said for the departed Bobby Wade.
"The punt return wasn't a problem (with Berrian)," Smith said. "We didn't hold our breath once he caught the ball, so that was big for him."