Taylor is expected to miss his team's matchup against the Tampa Bay Buccaneers in Week 4, sources told ESPN's Adam Schefter.
The 31-year-old was surprisingly ruled out prior to Week 2 after a team doctor accidentally punctured the signal-caller's lung before kickoff while trying to administer a pain-killing injection to Taylor's cracked ribs.
Doctors have advised Taylor to remain off the field indefinitely, and he was ruled out for Los Angeles' Week 3 matchup against the Carolina Panthers.
First-round rookie Justin Herbert took over under center in Taylor's absence, throwing for 311 yards and one touchdown against one interception during his NFL debut last week versus the Kansas City Chiefs.
Head coach Anthony Lynn said following the contest that Taylor is his starting quarterback when "he's 100% ready to go."