The person spoke on condition of anonymity because contract details were still being finalized and no official announcement was immediately planned.
Arizona spokesman Tom Duddleston said he had no information on a hiring and Athletic Director Greg Byrne did not immediately return phone messages.
Arizona fired coach Mike Stoops last month after he went 41-50 in seven-plus seasons at the Pac-12 school. The Wildcats have not won more than eight games in a season since going 12-1 in 1998 under Dick Tomey.
Rodriguez will try to change that with a fast-paced, spread attack that has produced prolific offenses everywhere he has coached.
But that wasn't enough in Ann Arbor.
He was fired by Michigan after last season, following three turbulent years. He went 15-22 with the Wolverines and the program was cited for rules violations by the NCAA during his tenure.
His last Michigan team went 7-6 — his only winning season there — but set numerous school records on the offensive side of the ball behind speedy quarterback Denard Robinson. And the team Rodriguez left behind for new Michigan coach Brady Hoke is 9-2 going into Saturday's game against Ohio State.
Before taking over the Wolverines, Rodriguez guided West Virginia to two BCS appearances.
Considered one of the pioneers of the spread offenses that have become so popular all over college football, Rodriguez went 60-26 in seven seasons at West Virginia.
With quarterback Pat White and running back Steve Slaton leading the way, the Mountaineers won the 2006 Sugar Bowl against Georgia and were a victory away from playing for the BCS championship in 2007. That opportunity slipped away when West Virginia was upset at home by Pittsburgh, and the loss set off the events that led to Rodriguez becoming Michigan's coach.
It was a messy divorce between West Virginia and Rodriguez. The school sued him to collect on the $4 million buyout clause in his contract, a lawsuit that was eventually settled.
Rodriguez has been working as an analyst for CBS Sports Network this year, but had made it clear he wanted to get back into coaching as soon as possible.
Byrne, in his second year as AD at Arizona, fired Stoops on Oct. 10, two days after the Wildcats lost to Oregon State 37-27.
The team was 1-5 at the time with the only victory over FCS member Northern Arizona. The Wildcats had lost 10 straight to FBS schools.
After five seasons of building the program, Stoops seemed to have the Wildcats back among the top teams in the Pac-10, leading them to a pair of eight-win seasons and trips to the 2008 Las Vegas Bowl and the Holiday Bowl the next year.
Arizona seemed poised to become one of the nation's elite teams by cracking the top 10 and opening 7-1 last season, igniting hope that the Wildcats could end their run as the only school from the league's Pac-10 days to not play in the Rose Bowl.
Then things started to fall apart.
The Wildcats lost their last five games in 2010, including a 36-10 blowout by Oklahoma State in the Alamo Bowl that came on the heels of a 35-0 rout by Nebraska in the Holiday Bowl the year before.
Stoops' contract ran through 2013 under an extension granted in 2008, and Byrne has said the buyout for the remainder of it will be about $1.4 million.
Stoops was 27-38 in conference games.
Defensive coordinator Tim Kish took over as interim coach and the team won two Pac-12 games, over UCLA and last Saturday 31-27 over rival Arizona State. The Wildcats (3-8) conclude their season Saturday at home against Louisiana-Lafayette.