Oliver, 29, played for Georgia from 2003-2006 and with the San Diego Chargers from 2007-11.
The San Diego Union-Tribune reported via Twitter that Oliver committed suicide. He died on Tuesday night.
“We appreciate all the thoughts and prayers,” said a statement from Oliver’s family to the newspaper via Twitter. “We request privacy in the wake of this tragic loss.”
Georgia coach Mark Richt said he got the news about Oliver on Wednesday.
“I was crushed this morning when I heard it, quite frankly,” Richt said. “I really haven’t been able to keep it off my mind to be honest with you.
“We’ve got to find a way to reach out and help in any way we can. If there’s some way that the Bulldog Nation can rally around that family I hope everybody would be encouraged to do so.”
Oliver was a five-star recruit and Parade All-American out of Harrison High School in Kennesaw. He played cornerback for Georgia.
Word of his passing reached former Georgia tailback Thomas Brown, now an assistant coach at Marshall. Brown said Oliver had moved back to Georgia.
“It was devastating to hear,” Brown said. “... He was always a very high-spirited guy (and) got along with everybody. I hate that I haven’t spent more time talking to him in the last few years. We got kind of separated because of different lives going on.”
Former Georgia defensive end Charles Johnson, now with the Carolina Panthers, tweeted: “Praying for my former teammate and a close friend, Paul Oliver #RIP #idontunderstandwhy”.
Oliver had seven interceptions and 94 tackles in his three seasons at Georgia after redshirting his first year.
“It was real frustrating, and at the same time, it was real humbling,” Oliver said in 2004 about redshirting. “It really made me go back and work a little harder and rethink things. In the long run, it really did help me out.”
Perhaps his best game with the Bulldogs in a 15-12 win over No. 16 Georgia Tech in 2006. Oliver held Calvin Johnson, now a star with the Detroit Lions, to two catches for 13 yards.
“We had a wolverine on Calvin Johnson the whole game,” defensive lineman Ray Gant said at the time. “Paul Oliver played like a champion today. He was on (Johnson) like white (on) rice.”
The Chargers selected Oliver in the fourth round of the supplemental draft after he became academically ineligible in the spring of 2007. He said at his personal pro day he felt like he let his coaches and teammates down after digging too deep a hole in the classroom.
Oliver had four interceptions and 144 tackles with the Chargers.