“We ask that everyone kindly respect Lea’s privacy during this devastating time,” the statement said, according to PerezHilton. com.
Monteith, 31, was found dead Saturday afternoon in a Vancouver hotel room.
He checked into the Fairmont Pacific Rim hotel on July 6 and was expected to check out on Saturday. When he didn’t, staff entered his room and discovered his body, Vancouver Police said.
Authorities have not yet determined the cause of death. They have ruled out foul play, and an autopsy is scheduled for Monday.
Both Monteith and Michele starred on the hit TV show "Glee," and the pair had been dating since early 2012.
Monteith recently completed a stint in rehab, during which time Michele expressed her “love and support” for him.
See celebrity reaction to Cory Monteith’s death
MORE: Twitter Reacts To Cory Monteith's Death