Elway was asked on 103.5 The Fox in Denver on Tuesday if he might still sign a veteran backup.
"I’m not going to tell you we’re definitely going to stand pat, but I’m not telling you we’re going (in) that direction, either," Elway said, according to Arnie Stapleton of The Associated Press.
On Monday, Broncos head coach Vance Joseph announced that second-year quarterback Chad Kelly would be replacing Paxton Lynch as the teams backup. Kelly, a seventh-round pick of Denver in 2017, didn't play a single down last season.
In the Broncos' preseason opener, Kelly completed 14 of 21 passes for 177 yards while throwing two touchdowns and an interception.
Lynch, 24, was the 26th overall selection of the 2016 draft. He's completed 79 of 128 attempts over five career games and thrown four touchdowns and four interceptions.
Though Keenum has never missed time due to injury, Elway doesn't want to take any chances.
"We’ve got to have confidence that that guy that’s going to be the backup can play and win football games," Elway said. "And so that’s why we’re still in that process of trying to see if we’ve got that guy behind Case."