The Raiders also are said to be considering another coach, but the fact that Allen is thought to be the first candidate asked to interview a second time is a sign he is one of the favorites, if not the favorite, for the job.
Allen's second interview with the Raiders is expected to take place this week at the Senior Bowl in Mobile, Ala.
Allen also interviewed for the Rams' job that went to Jeff Fisher. A St. Louis source was highly impressed with the Broncos assistant.
Denver officials have believed Allen would become an NFL head coach in the near future, just maybe not in this offseason.
The Raiders, hoping to make the hire by the end of the week, already have interviewed Green Bay Packers assistant head coach Winston Moss, Philadelphia Eagles offensive coordinator Marty Mornhinweg, New Orleans Saints offensive coordinator Pete Carmichael Jr. and former Miami Dolphins secondary coach Todd Bowle.
Chicago Bears offensive coordinator Mike Tice was expected to meet with Oakland officials Tuesday at the Senior Bowl. But the Bears said Monday that interview won't take place because the Raiders have moved onto the "second phase" of their interview process.
Adam Schefter is ESPN's NFL Insider. Information from The Associated Press contributed to this report.