The team said Sunday that Riley informed the club of the threats and did not know who made them. The team has notified the league's security department.
Cooper was fined by the Eagles after his slur became known Wednesday. He left the team Friday to seek counseling.
"Riley Cooper made us aware of the tweets when the video became public," the team said in a statement. "He told us that he did not know about the video. He informed us he blocked the tweets because he did not know the person nor understand the context of what that person was threatening.
"We promptly alerted NFL security. This information potentially speaks to a legal issue that is a matter between Riley and the authorities. Our focus has been on Riley's words and actions."
The video of Cooper was taken at a Kenny Chesney concert in June. Cooper apologized profusely both Wednesday and Thursday.
Eagles coach Chip Kelly has said Cooper's roster spot is not in jeopardy. Cooper has just 46 catches and five touchdowns in three years with the Eagles, but had been practicing with the starters after Jeremy Maclin's season-ending knee injury.
Asked when Cooper will return to the Eagles, Kelly said there's no time frame.
"When we do, we'll make sure we announce it so it's not going to be a surprise to anybody," Kelly said.