Attorney Ken Feinberg told The Associated Press that he delivered the demands to Penn State administrators, lawyers and members of the board of trustees during a meeting Friday in Philadelphia.
"The next step is Penn State - we'll see how Penn State responds in the next few weeks," Feinberg said.
Asked about the meeting, a university spokesman declined to comment. Reactions by lawyers for the claimants ranged from hopefulness to no comment. None would say what dollar figure he or she is seeking.
Feinberg "has assured us that within a degree of somewhat certainty, like 85 percent, he thinks he can get our case settled," said Harrisburg attorney Chuck Schmidt, whose client's lawsuit is on hold. "So far as it moving forward, I'm cautiously optimistic."
Bala Cynwyd lawyer Mike Boni, who represents Aaron Fisher, the young man whose story launched the investigation into Sandusky and who wrote a book about the abuse, said Feinberg's response to his settlement offer was "hope springs eternal."
"He said what he had to say, which is, 'You're asking for too much, I'll see what I can deliver,'" Boni said. "At the end of the day, I don't think we're all that far apart."
Sandusky, 69, is serving a 30- to 60-year prison term for the sexual abuse of 10 boys over 15 years, including attacks on children inside Penn State athletics facilities. Penn State's president issued a statement the day Sandusky was convicted in June, vowing to settle "privately, expeditiously and fairly."
Feinberg disclosed last month that he was working with 28 claimants, 18 more than were the subject of Sandusky's criminal trial. He emphasized Monday that not all claimants have made settlement demands.
Also Monday, a Penn State trustee called on the university governing board to re-examine the findings of former FBI director Louis Freeh's school-sanctioned investigation into the scandal.
A critique released this weekend by Joe Paterno's family raised "serious and troubling" questions about Freeh's findings, trustee Alvin Clemens said in a statement.
Former U.S. Attorney General Dick Thornburgh was among the experts brought in by the Paterno family to review the Freeh report, which concluded that Paterno and other university officials covered up allegations against Sandusky to spare the university bad publicity. The family's review said the cover-up claims were inaccurate, were unfounded and equated to a "rush to injustice."
Freeh has defended his work and stood by his findings. He has called the Paterno family's review self-serving and a campaign to shape the late Hall of Fame coach's legacy.
Paterno died in January 2012 at age 85.
The NCAA levied unprecedented sanctions on Penn State less than two weeks after Freeh released his stinging findings in July.
Freeh's firm was hired by the board of trustees to perform "an independent, full and complete investigation of the Sandusky scandal," said Clemens, a trustee since 1995. "In addition to questions about accuracy and fairness, there is little question that the Freeh report is less than complete."
Through a spokesman, the school declined comment on Clemens' request.
Penn State had said Sunday that Freeh was brought in to conduct an independent investigation of the school's response to the allegations, and not actions of entities unrelated to Penn State. Freeh offered 119 recommendations to strengthen governance and compliance, the majority of which have been implemented, the school said.
Freeh's report has never been formally discussed by the board as a whole. At the time of its release, trustees said they had accepted responsibility for failures of accountability.
The public should devote equal time reading the Paterno family's critique and the Freeh report, said another trustee, former football player Adam Taliaferro. He joined the board last summer, but was not a trustee at the time of Paterno's firing in November 2011.
In a phone interview, Taliaferro said Monday the board was off to a good start in implementing Freeh's recommendations. "But for me, personally, it wouldn't hurt for us to look at both sides ... There are always two sides to a story," he said.
Paterno's family offered its answer to the Freeh report on Sunday, with experts attacking what they called flawed techniques and a lack of evidence.
Paterno's widow, Sue, and three of the Paternos' children spoke with Katie Couric in an interview that aired on her syndicated TV show Monday. Former NFL linebacker and Nittany Lion standout Greg Buttle defended Paterno on the program as someone who would have taken issue and "taken care of it" if the coach knew of Sandusky's crimes.
"Joe Paterno didn't conspire to do anything," Buttle said. "The conspiracy to me was perpetrated by a cabal of trustees, and others that felt they needed a convenient way out to relieve Penn State of what had happened."
Armas reported from State College, Pa.