Monteith, 31, was found dead in a Vancouver hotel on Saturday, People magazine reported.
The 26-year-old Michele's representatives said, "We ask that everyone kindly respect Lea's privacy during this devastating time. Thank you."
Michele had supported Monteith's decision to enter rehab for substance addiction on March 31.
For his part, Monteith, a Canada native, was visiting his mother in t he Vancouver area at the time of his death.