Allen, 48, is a former NBA point guard who has been an assistant with the Celtics since 2015. Boston is undergoing a coaching search after Brad Stevens replaced Danny Ainge as president of basketball operations.
Along with Allen, the Celtics are expected to interview assistant Scott Morrison.
Allen played for the Timberwolves, Pacers and Nuggets from 1995-97, then headed overseas before retiring in 2009. He compiled a 65-104 record as coach at Penn from 2009-15.
Fellow Celtics assistant Jay Larranaga also has been mentioned as a candidate, as have ex-Hawks coach Lloyd Pierce, Lakers assistant Jason Kidd, Clippers assistant Chauncey Billups and Nets assistant Ime Udoka.