No official offer has been made, a source close to the coaching search told the Birmingham News on Saturday, though Arkansas coach Bobby Petrino issued a statement in the morning congratulating McGee on landing the job.
A UAB spokesman told The Associated Press he hasn't heard of a hiring.
McGee is a former Oklahoma quarterback and Jacksonville Jaguars assistant. He would be replacing Neil Callaway, who was fired Nov. 27 after UAB lost to Florida Atlantic 38-35 and finished the season 3-9.
McGee, who also coaches quarterbacks, is in his fourth season with the Razorbacks and is a finalist for the Broyles Award, which is given
to the nation's top assistant.
Arkansas' offense has blossomed the past two seasons under the guidance of McGee, and the Razorbacks made their first BCS bowl appearance last season.
"I thank him for being a big part of everything we have been able to build here at Arkansas," Petrino said in his statement. "The guidance he has provided our offense and quarterbacks the past four seasons has been immeasurable."
McGee has tutored players such as Ryan Mallett -- who was taken in the third round of June's draft by the New England Patriots -- and current Razorbacks quarterback Tyler Wilson, who led the team to a 10-2 overall record, 6-2 in the SEC.
Arkansas leads the conference in total and passing offense this season and is second in scoring.
McGee also has coached at Toledo and Northwestern.
Joe Schad covers college football for ESPN. Information from The Associated Press was used in this report.