Allen is projected to get the start in goal in Thursday's road clash with the Canucks, Stu Cowan of The Montreal Gazette reports.
Allen will tend the road twine in Monday's game against the Oilers, John Lu of TSN.ca reports.
Canadiens goalie coach Stephane Waite projects Allen to play 30 games if the NHL has a regular 82-game schedule, Pat Hickey of the Montreal Gazette reports.
Allen penned a two-year, $5.75 million contract extension with Montreal on Wednesday.
Allen was brought in by the Canadiens from the Blues, along with a 2022 seventh-round pick, in exchange for 2020 picks in the third and seventh rounds.
Allen will be the backup to Jordan Binnington in Friday's Game 6 against the Canucks, Jeremy Rutherford of The Athletic reports.
Allen led the Blues onto the ice and will start Game 5 versus the Canucks on Wednesday, Thomas Drance of The Athletic Vancouver reports.
Allen will be stationed between the pipes for Monday's Game 4 tilt with Vancouver, Jeremy Rutherford of The Athletic reports.
Allen will patrol the blue paint for Sunday's contest against the Canucks, Thomas Drance of The Athletic Vancouver reports.
Allen yielded one goal on 38 shots in Sunday's 2-1 round-robin shootout loss to the Stars.