"We ask that everyone kindly respect Lea's privacy during this devastating time," the actress' rep toldPeople.
Monteith was found dead in a Vancouver hotel room on Saturday. He was 31. A cause of death has not been determined yet.
In April, Monteith's rep announced that the actor had voluntarily entered a rehab facility for substance abuse treatment. At the time, Michele threw her support behind Monteith, telling People, "I love and support Cory and will stand by him through this."
At the end of May, Monteith thanked fans for their support on Twitter: "sending out big love to everyone. thank you for the continued support! It means the world to me!" Micheletweeted, "Today is a great day :) Love you all! Xo."
Michele and Monteith started dating while starring together on the Fox show, "Glee." Their on-screen characters had an on and off romance over the years, filling out one of the major -- and most interesting -- plot lines on the Fox series.