The network released a statement Friday saying production was initially scheduled to begin in late July, but will now start in August, The Hollywood Reporter said.
The series season premiere was rescheduled from Sept. 13 to Sept. 26, TMZ reported.
Producers haven't said how or whether they will address Monteith's death or how they plan to write out his character, Finn Hudson, The Hollywood Reporter said.
The series has a history of tackling tough subject matter, including teen pregnancy and school shootings.
Monteith died July 13 at age 31 in a hotel room in Vancouver. The British Columbia Coroner's Service said he died of "mixed-drug toxicity, involving heroin and alcohol.