Allen (shoulder) played 15 of the Rams' 65 snaps on offense and went without a target in Thursday's 12-6 win over the 49ers.
Allen (shoulder) did not practice Tuesday.
Allen wasn't targeted during Sunday's 28-22 victory against the Patriots.
Allen secured five of six targets for 34 yards during Sunday's 23-15 loss to the Dolphins.
Allen (back) is active Sunday against the Bears.
Allen (back) is questionable for Sunday's game against the Bears, Jourdan Rodrigue of The Athletic reports.
Allen (back) was a limited participant at the Rams' practice Wednesday, Adam Grosbard of The Orange County Register reports.
Allen (back) has been ruled out for Sunday's game against San Francisco, Gary Klein of the Los Angeles Times reports.
Allen (back) is listed as doubtful ahead of Sunday's contest against the Cardinals, Josh Weinfuss of ESPN.com reports.
Allen looks to be ahead of Hunter Long in a competition for the No. 2 TE spot early in the season, according to Cameron DaSilva of Rams Wire.