"His family will have no comment on the situation and asks that their privacy be respected during this difficult time," he said.
Paterno's sons Scott and Jay each took to Twitter Saturday night to refute reports that their father had died.
Wrote Jay Paterno: "I appreciate the support & prayers. Joe is continuing to fight."
The 85-year-old Paterno has been in the hospital since Jan. 13 for observation for what his family had called minor complications from his cancer treatments. Not long before that, he conducted his only interview since losing his job, with The Washington Post. Paterno was described as frail then and wearing a wig. The second half of the two-day interview was conducted by his bedside.
Roughly 200 students and townspeople gathered Saturday night at a statue of Paterno just outside a gate at Beaver Stadium. Some brought candles, while others held up their smartphones to take photos of the scene. The mood was somber, with no chanting or shouting.
"Drove by students at the Joe statue," Jay Paterno tweeted. "Just told my Dad about all the love & supportinspiring him."
The final days of Paterno's Penn State career were easily the toughest in his 61 years with the university and 46 seasons as head football coach.
Sandusky, a longtime defensive coordinator who was on Paterno's staff during two national title seasons, was arrested Nov. 5 and ultimately charged with sexually abusing a total of 10 boys over 15 years. His arrest sparked outrage not just locally but across the nation, and there were widespread calls for Paterno to quit.
Paterno announced late on Nov. 9 that he would retire at the end of the season but just hours later he received a call from board vice chairman John Surma, telling him he had been terminated as coach. By that point, a crowd of students and media were outside the Paterno home. When news spread that Paterno had been dumped, there was rioting in State College.
Police on Saturday evening had barricaded off the block where Paterno lives, and a police car was stationed about 50 yards from his home. Several people had gathered in the living room of the house. No one was outside, other than reporters and photographers stationed there.
Trustees said this week they pushed Paterno out in part because he failed a moral responsibility to report an allegation made in 2002 against Sandusky to authorities outside the university. They also felt he had challenged their authority and that, as a practical matter, with all the media in town and attention to the Sandusky case, he could no longer run the team.
Paterno testified before the grand jury investigating Sandusky that he had relayed to his bosses an accusation that came from graduate assistant Mike McQueary, who said he saw Sandusky abusing a boy in the showers of the Penn State football building.
Paterno told the Post that he didn't know how to handle the charge, but a day after McQueary visited him, he spoke to the athletic director and the administrator with oversight over the campus police.
Wick Sollers, Paterno's lawyer, called the board's comments this week self-serving and unsupported by the facts. Paterno fully reported what he knew to the people responsible for campus investigations, Sollers said.
"He did what he thought was right with the information he had at the time," Sollers said.
Sandusky says he is innocent and is out on bail, awaiting trial.