Following the shocking death of Cory Monteith, Glee producers are working internally to figure out how they'll handle his character's departure on the hit FOX show.

"The show will go on, but writers and producers have to figure out how his character Finn be written out," a source close to the show told EnStars.

Monteith’s final episode, which aired April 18, focused on Finn and Puck partying like typical college students at the University of Lima. At one point, Finn said, “I have the rest of my life to be a grown-up and for now, it’s OK to have fun.”

While producers want to be "as sensitive as possible," they may use Monteith's death as an opportunity to explore the hazards of drugs and alcohol, the source added.

The show was set to begin filming season five next week.

As EnStars previously reported, Monteith's girlfriend and Glee co-star Lea Michele is grieving with his family.

"Lea is deeply grateful for all the love and support she's received from family, friends, and fans. Since Cory's passing, Lea has been grieving alongside his family and making appropriate arrangements with them," read the statement, obtained by PEOPLE. "They are supporting each other as they endure this profound loss together. We continue to ask the media to respect the privacy of Lea and Cory's family."

Monteith was found deceased in his room at the Fairmont Pacific Rim hotel in downtown Vancouver, British Columbia, shortly after noon on July 13. He had checked into the hotel on July 6 and had been expected to check out on the 13th. When he had not done so, hotel staff checked his room and found him deceased.

On Tuesday, July 16, the coroner announced that Monteith died from a lethal mixture of heroin and alcohol. The post-mortem testing, which included an autopsy and toxicological analysis, seem to confirm this was an accident.

Monteith entered rehab earlier this year for substance abuse, after previously seeking help for addiction at age 19.

The new season of Glee debuts on September 19 on FOX.

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Glee, Lea michele, Cory Monteith