Coach Mike Shanahan was hopeful on Friday that both players will be able to assume backup roles to Gus Frerotte and Mike Anderson, respectively.
Griese missed his third straight day of practice because of torn cartilage in his throwing shoulder. Earlier in the week, Shanahan said the best-case scenario was for Griese to rest his shoulder and try to throw on Friday, but the league's top-rated passer was held out of the drills partly because of cold, drizzly weather.
Frerotte, a seven-year veteran who has not thrown a pass this season, will get his first start since the Detroit-Washington NFC playoff game last January.
Davis, who has missed the past two games with a sprained left ankle, practiced on a limited basis and showed some improvement Friday. But Anderson, a sixth-round draft choice who has rushed for 131 and 187 yards in Davis' absence, will get his third consecutive start.
"Brian's shoulder is better," Shanahan said. "The inflammation is a little bit down, the pain has subsided. I just didn't want to push it, especially in this weather. He couldn't go full speed, by any means. We told him not to even try it. I was afraid if he did try to throw, he might inflame that area.
"Gus will start, but hopefully Brian will be able to play in a backup role if it's feeling better. We'll give it a couple days of rest to see how he's able to throw before the game."
If Griese isn't recovered, rookie Jarious Jackson will be Frerotte's backup.
"I've prepared like I'm going to start," Frerotte said. "I feel real good. I've had a good week of practice."
Shanahan said naming Frerotte the starter now rather than waiting until Sunday "helps the team in general. We're saying, `Hey, this is the direction we're going to go. Gus, you're the guy.' He's had a great week of practice. His teammates have got a lot of confidence in him, he's been there before and he gets a chance to show what he can do."
Davis, whose steady recovery from reonstructive surgery on his right knee last October was slowed by the ankle injury he suffered in the season opener, ran hard on Friday.
"He looked pretty good today," Shanahan said. "It's the best he's looked. Hopefully, he'll get some playing time if he keeps on improving.
"I'd say he'll probably play in the area of 20 plays during the game. That would give him a chance to play some maybe 10 carries."
If Davis is unavailable, veteran Raymont Harris will back up Anderson.
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