Monteith, who portrayed Finn Hudson on the show, was found dead in his hotel room at Vancouver's Fairmont Pacific Rim in Canada, and his co-stars flooded social networking sites to mourn the actor's passing.
Now Paltrow, who played substitute teacher Holly Holliday in Glee, has expressed her heartache over the loss of her friend and for his girlfriend, Lea Michele.
She has released a statement which reads, "Cory was a sweet and talented man. My heart breaks for Lea and the entire Glee family."
A publicist for Michele, who played Monteith's onscreen on/off girlfriend Rachel Berry on the series, has asked for the public and the media to respect her privacy as she mourns her boyfriend.