Redd will travel to California for a visit Saturday, a source said, and may decide on whether he will leave Penn State by Monday.
Redd, Penn State's leading rusher last season, is intrigued by the chance to compete for a national championship and that could overwhelm the emotional part of him wanting to stay for his teammates, the source said.
Redd has two years of eligibility remaining; he would plan to play at USC for both seasons, but could turn pro after this year if he was judged to be a first-rounder. USC laid out an extensive presentation on how Redd would fit with the team, including Power Point presentation and video clips.
The NCAA has said players can transfer from Penn State and be eligible immediately.
One USC player, quarterback Max Wittek, has joined Kiffin in the recruitment of Redd.
Wittek, who grew up in Connecticut and played Pop Warner football with Redd, called the running back earlier this week, he told the Los Angeles Times.
"I told him I was sorry to hear about everything that came down and that it was obviously a difficult situation," Wittek told the newspaper. "But I tried to sell USC to him a little bit. I'd love to have him here.
"He said thanks for reaching out, that he was definitely interested and was just trying to take the right steps to decide what he was going to do."
While Kiffin was returning to California, Penn State coach Bill O'Brien was at the podium Thursday at Big Ten media days in Chicago. Asked if he had an update on Redd, O'Brien said, "No."
Redd originally was scheduled to attend the media days, but three other Penn State players were brought to Chicago instead.
On Wednesday, Penn State had decided not to bring any players to the event, but the Nittany Lions changed course Thursday, bringing linebacker Michael Mauti, defensive lineman Jordan Hill and guard John Urschel.
Mauti said Thursday that he hopes Redd "makes the right decision."
Redd was not among the players who gathered Wednesday in State College, Pa., to announce their support of the embattled football program.
Redd, 5-foot-10 and 209 pounds, ran for 1,241 yards and seven touchdowns last season.
Any transferred Penn State player who gets a scholarship does not count against another school's scholarship total. However, the NCAA has clarified that a school "subject to scholarship limits due to an infractions case is allowed to accept transfers from Penn State but cannot exceed the scholarship limits specified in its infractions report."
USC, which was sanctioned by the NCAA in 2010 over improper benefits, is at its limit of 75 players, so a spot would have to open up for Redd to transfer to the school. USC believes at least one player will be academically ineligible, opening up a spot for Redd. The backup plan would have a walk-on giving up a scholarship.
O'Brien said the recruiting frenzy has led to "an NFL free-agent system." Immediately after the NCAA sanctions were announced Monday, O'Brien held a team meeting preaching togetherness and the challenge of overcoming adversity. But he acknowledged Wednesday he had not anticipated that other schools would push this hard for every player on his team.
"These kids don't want to leave Penn State," O'Brien said. "They want to play for Penn State. It is my opinion these coaches should leave them alone, but if they don't want to leave them alone, they should make sure they give me a call before they try to recruit them."
ESPN.com's Don Van Natta Jr. contributed to this report.