The interview was scheduled to take place at Pepsi Center in Denver, the source said. The official noted that the team's game plan and film preparation is completed, allowing Allen to do the interview.
Allen will be with the team for its walkthrough Friday morning before it leaves for New England to play the Patriots Saturday night.
The Rams also have interviewed front-runner Jeff Fisher, who's expected to pick between St. Louis and the Miami Dolphins this week.
The Rams are scheduled to interview Carolina Panthers offensive coordinator Rob Chudzinski on Thursday, a league source told ESPN NFL Insider Adam Schefter.
St. Louis plans to interview New Orleans Saints assistant coach Aaron Kromer Friday, league sources said.
Allen revamped a defense that was among the league's worst a season ago.
"In my mind, it's more of a tribute to those players that are in that locker room," Allen said Wednesday of the interview opportunity. "It's a tribute to the assistant coaches that I work with every day. When you have success as a team, individual achievements come.
"At the end of the day, my focus is to try to win a game against the New England Patriots, and that's the only thing that I'm concerned with right now."
Information from ESPN's George Smith and The Associated Press was used in this report.