No foul play is suspected, Boulder police spokeswoman Shannon Cordingly said. She said the cause of death is under investigation. An autopsy was to be performed.
USA Today reported that Salaam's mother, Khalada Salaam, said that police told her they suspect the death is a suicide.
"They said they found a note and would share that with us when we get there," she told USA Today. CNN called Khalada Salaam on Tuesday night but didn't get a response.
Rashaan Salaam was found in Eben B. Fine Park just before 9 p.m. Monday.
"He had a happy heart. I loved being around him," former Colorado Coach Bill McCartney told CUBuffs.com. "He didn't take himself too seriously, and he always credited those around him, especially his offensive line. What I liked about him is that he had a sparkle in his eye. He was upbeat and positive."
Salaam led the Buffaloes to a No. 3 finish nationally in 1994 as a junior. He rushed for 2,055 yards and easily won the Heisman Trophy over running back Ki-Jana Carter of Penn State.
Former teammate Chad Brown said he was "beyond saddened."
"We lost a true Buffalo today," he tweeted.
A family member of Salaam told CNN on Wednesday they do not plan to have a private autopsy or have his brain tested for chronic traumatic encephalopathy, known as CTE, a neurodegenerative disease associated with repeated head trauma.
Salaam was the youngest NFL player to reach 1,000 yards rushing and was NFC Rookie of the Year in 1995, but he played just 33 games in his pro career. According to CUBuffs.com, he was slowed by ankle and knee injuries.
Salaam played in the short-lived XFL and the Canadian Football League.