Floyd met Wednesday afternoon with Arizona athletic director Jim Livengood to work out the final details of the deal, according to Mark Asher of Sports 620 KTAR, ESPN Radio's affiliate in Phoenix, and the Los Angeles Times.
The Tucson Citizen reported that Floyd left in the evening to return to Los Angeles.
According to the Times, Floyd has 24 hours to make a decision.
On Tuesday, the Wildcats had requested permission from USC to speak with Floyd, which was granted by athletic director Mike Garrett.
That night, according to the Times, during the USC team banquet, Floyd said the players had a chance to win a national title if they stayed at USC, instead of leaving early to go to the NBA.
"He was just saying that we would have a good year next year and that he believed in us, and that he thinks we could make a Final Four run," USC guard Marcus Simmons told the Times.
Simmons also said he did not know what was going on with his coach and the future.
"He hasn't shown any signs at all," Simmons said, the Times reported. "When you talk to him, you would think he's staying here forever. No sign at all. I'm clueless right now as to what's going on."
Last year, when Louisiana State pursued Floyd, he said at the time that USC would be his last job.
Messages left for Livengood on his cell phone by The Associated Press were not returned.
Arizona sports information director Tom Duddleston said Thursday no news conference or announcement had been scheduled.
Garrett told the Times that Floyd will "come to me and tell me what he's decided. That's how it works."
Garrett added, according to the Times: "If people don't want to be here they can go somewhere else. And if Tim has decided that, I thought he was a great coach and we've just got to find another great coach."
Garrett was unavailable for comment Thursday, USC sports information director Tim Tessalone said. Tessalone had no comment on the Floyd report.
Floyd, 55, has led the team to an NCAA berth in each of the past three seasons, and is 85-50 in his four years at USC.
If Floyd accepts the Arizona job, he would replace Russ Pennell, who stepped in as coach after Lute Olson retired for health reasons.
Floyd previously coached in the NBA with the Chicago Bulls from 1999 to 2002 and the New Orleans Hornets in 2004.
He was also the head coach at Iowa State, New Orleans and Idaho.
Information from The Associated Press was used in this report.