The Tennessean said Franklin was expected to meet with athletics director David Williams and John Ingram, a man described by the newspaper as "one of the university's most generous donors and influential people."
"We love James and we're fighting hard to keep James, and we're going to do everything that we can to do that," Ingram told the Tennessean. "These situations don't age well for anybody. I think the coach needs to make a decision. . . . We certainly look forward to an opportunity to reiterate to James how much we'd like him to stay."
Williams and Ingram did not return calls to The Tennessean seeking comment on the meeting.
News of the imminent hiring spurred a professor to start a petition on Change.org urging the board of trustees to reject Franklin.
Michelle Rodino-Colocino, an associate professor in the department of film-video and media studies and an affiliate faculty member in the department of women's studies, cited the case in which four Vanderbilt football players were charged with raping and sexually assaulting a female Vanderbilt student last year. A fifth player pleaded guilty to trying to cover up the attack.
In her post on Change.org, Rodino-Colocino said the school should not hire a coach "who has allegedly covered up his players' gang rape of another student at Vanderbilt. Our university needs to stand up for human rights."
The five players were dismissed from the team, and the prosecutor in the case said he found no evidence Franklin was involved in a cover-up of the attack. A trial of the four accused players is scheduled to begin in August.
Franklin, a star quarterback at East Stroudsburg in the early 1990s, led Vanderbilt, usually the weak link in the strong SEC, to 24 victories in three seasons, all of which ended with a bowl game. He has been described by friends as "energetic" and "passionate" and is considered an offense-minded coach and a fine recruiter.
One of his first tasks would be to address the Nittany Lions' 2014 recruiting class and convince them to keep the commitments they made to O'Brien and his staff.
One recruit, four-star quarterback Michael O'Connor of Bradenton, Fla., had expressed doubts about early enrollment at the university next week but now says he will speak with Franklin before making a final decision, according to Blue White Illustrated.
Franklin also must persuade the doubters in the Penn State community concerning the Vanderbilt rape case.
The anticipated hiring of Franklin ended a nine-day search that included interviews by Penn State's six-member search committee, chaired by athletic director Dave Joyner, with Franklin, Miami coach Al Golden, former Tennessee Titans coach Mike Munchak, San Francisco 49ers offensive coordinator Greg Roman, and Nittany Lions interim head coach Larry Johnson, according to reports.
Franklin and Roman were the only candidates interviewed who did not have previous ties to Penn State.
Franklin emerged as the clear-cut favorite and on Wednesday, university president Rodney Erickson, Joyner, and other Penn State officials met with him at his vacation home in Destin, Fla. During that meeting, Franklin reportedly was offered the job.
Two websites, ESPN.com and CBSSports.com, said Thursday that Franklin was "expected" to accept the offer. The holdup presumably was because the compensation committee of Penn State's board of trustees still had to approve the contract.