Sandusky, who is awaiting trial, has maintained his innocence.
A school spokesman, Bill Mahon, said Monday that university attorneys did not discuss the naming issue with Paterno representatives in the course of wrapping up the contract. The person familiar with the issue said no formal offer was ever made.
The Patriot-News of Harrisburg first reported about the topic Sunday.
The school was turning over four checks worth more than $3 million for bonuses that covered the season, bowl game and entire career, a university spokeswoman said last week. The breakdown provided by Penn State also included the use by Paterno's family of a Beaver Stadium suite for 25 years and $900,000 from television and radio revenue from last season.
Paterno family lawyer Wick Sollers said Thursday it was not a settlement but rather "a straightforward payment of moneys indisputably owed to the Paterno estate."
The family declined a request to a full release in return for the payments under the contract, Sollers said. Without a release, Paterno's estate could still sue under the contract or some other reason, if it wishes.
The university on its "openness" website Monday stated that neither the board, nor its attorney ever discussed the possible renaming of the stadium in connection with talks about making payments under Paterno's contract. The school also called false a report that the board or its attorney tried to leverage a stadium name change in connection with the contract discussions.
Beaver Stadium is named after James A. Beaver, a Pennsylvania governor and superior court judge, and former president of the Board of Trustees. He died in 1914.
An alumni-driven effort to rename the field at Beaver Stadium after Paterno sprouted a few years ago. The issue came up sporadically in Paterno's discussions with reporters in recent years, during which the coach typically said he wasn't interested or downplayed such questions.