Monteith, who also played Michele's on/off boyfriend on Tv show Glee, was found dead in a hotel room at Vancouver's Fairmont Pacific Rim in Canada on Saturday afternoon (13Jul13).
Stars have flocked to social media outlets like Twitter and Facebook to pay their respects to the tragic 31 year old and to ask their fans to pray for Michele, and now her representative has released a short statement, which reads: "We ask that everyone kindly respect Lea's privacy during this devastating time."
The actress, 26, was helping Monteith overcome addiction issues following a stint in rehab in the spring (13). When news broke of his treatment, she told People magazine, "I love and support Cory and will stand by him through this."
Monteith spent a month in rehab and appeared to be in positive spirits when he checked out in April (13), tweeting, "Sending out big love to everyone. thank you for the continued support! It means the world to me!"
His Glee co-stars Kristin Chenoweth and Dot-Marie Jones were among the first celebrities to take to Twitter to pay tribute to the actor.
Jones wrote, "Cory was not only a hell of a friend, he was one amazing man that I will hold close to my heart forever. I am blessed to have worked with him and love him so much."
And a statement from Fox, the Tv network behind Glee, issued a statement calling Monteith "an exceptional talent and an even more exceptional person".
Other Glee co-stars who have offered up their thoughts on Twitter include Damian MCGinty, Mark Salling and Iqbal Theba, who plays Principal Figgins on the show - he wrote, "Omg!! My Cory...", while Neil Patrick Harris added, "How sad to read about Cory Monteith passing away. What a shame. He was a lovely, kind, talented guy and will be missed."
Rihanna and Mia Farrow have also added their tributes on the micro-blogging website.
The singer writes, "Cory Monteith, may your spirit be at peace, and may you fly with the angels... Heartbreaking, my prayers are with all of his loved ones!"
And actress Farrow adds, "Rest in peace Cory Monteith. Sad, very very sad."
One Direction singer Niall Horan also took to Twitter to pay his respects, describing Monteith as a "super nice guy".