Siemian was the "clear-cut winner" in his competition with Paxton Lynch for the starting job, Joseph said.
Denver split reps between the two over the first preseason games with Siemian starting the first and Lynch starting the second.
San Francisco's Brian Hoyer was 8 of 11 for 89 yards and an interception while garnering a 58.5 passer rating. He successfully ran the two-minute drill in last Saturday's win over the 49ers, capping the drive with a 19-yard touchdown pass to Jordan Taylor.
In two preseason games, Siemian is 14-of-18 for 144 yards and the touchdown pass for a 118.5 passer rating.
"The time frame's not important", Joseph said. He threw for 3,401 yards to go with 18 touchdowns and 10 interceptions.More news: Saints practice with the Chargers
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"Well, I saw Paxton make some plays with his legs, which he should".
Siemian said he thought he had done enough to be the starter.
Joseph told reporters that the Broncos are all in agreement with the decision.
"Decision-making and ball placement was more consistent with Trevor". "I'm not the coach but I think so".
Broncos coach Vance Joseph is expected to deliver the news when he meets with the media later Monday.
"I'm not sure, once we watch this tape and see where we are with that", Joseph said on KUSA's television broadcast.