The university released no dollar amounts, but noted that "a range of dollar values" was shared with the board in "confidential, attorney-client privileged session" June 25 and again Friday morning.
The university emphasized that no settlement agreements had been signed and gave no timetable for the process to be completed, but said it hoped it would be in the next several weeks.
"Today's action is yet another important step toward the resolution of claims from Sandusky's victims," president Rodney Erickson said in a statement.
Board chairman Keith Masser and other trustees declined to provide any specifics about the potential settlements, such as how many there are or how many would be settled. When the settlements are final, the university will release the total amount that victims will be paid, a spokesman said.
"We're chipping away at getting these issues behind us," Masser said at a news conference. "And every one we get behind us allows us to keep looking forward."
The total number of victims that have come forward with claims is believed to be over 30, including the eight young men who testified against Sandusky at his trial last summer.
It is anticipated that settlements with some victims could be in the seven-figure range, while others may be smaller.
Legal analysts have estimated that Penn State's legal liability could exceed $100 million if the cases were to go to trial.
University officials said they would have no further comment until the process is complete.
Thomas R. Kline, a Philadelphia lawyer who represents the 26-year-old man known in the Sandusky court filings as Victim Five, called the board's action a "positive step."
"I expect further progress in the weeks ahead toward settlement," Kline said.
Kline said he expects his client will be part of a larger settlement "if the process continues on its current track."
He would not divulge any of the terms or amount of his case or the global settlement.
On Thursday, ousted university president Graham B. Spanier filed a notice of intent to sue former FBI Director Louis Freeh, whose university-commissioned report said Spanier and other leaders conspired to cover up Sandusky's abuse. Spanier lost his job in November 2011 after the grand jury presentment against Sandusky.
Spanier, former athletic director Tim Curley, and former vice president Gary Schultz face trial on perjury and other charges in the case.
Their preliminary hearing date was set this week for July 29 in Dauphin County Court.
Announcement of the tentative settlement with Sandusky's victims comes on the first anniversary of the Freeh report, which found university leadership culpable for allowing Sandusky's abuse to continue for years.
Sandusky was sentenced in October to a minimum of 30 years in prison for abusing 10 boys over 15 years. The abuse occurred on and off campus. At the trial last summer, victims described how Sandusky fondled and raped them when they were young.
Also at Friday's trustees' meeting, the board approved a $4.4 billion budget, including an average 2.76 percent tuition hike for students. The percentage of the tuition hike varies by campus, with in-state students at the main campus paying 3.39 percent more.
The board also elected Paul Silvis, founder of Restek Corp., a chromatography company, as its new vice chair. Silvis, of State College, has been on the board since 2010. He beat out Ryan J. McCombie, a retired Navy SEAL captain, also from State College.
Contact Susan Snyder at 215-854-4693 or firstname.lastname@example.org or follow on Twitter @ssnyderinq. Read her blog at http://www.philly.com/philly/blogs/campus_inq.