The "Glee" star, who had a history of substance abuse, was found dead in his Vancouver hotel room Saturday.
An autopsy is scheduled for Monday to determine the cause of death.
UsMagazine.com said Michele, 26, has declined to comment on the death of her boyfriend of a year.
"We ask that everyone kindly respect Lea's privacy during this devastating time," her publicist said in a statement to UsMagazine.com.
Michele was not with Monteith when he died, but a friend told the New York Daily News she "is devastated" by the loss.
"She was shaking when she heard the news," the unnamed source said.
Matthew Morrison spoke about Monteith at his New York nightclub show "Up Close and Personal with Matthew Morrison" Sunday.
"Matt came out before the show started and said, 'We lost a great young man too soon,'" a source told the magazine.
"He said Cory was a beautiful person," the insider reported, adding Morrison told the crowd, "You came out to see a show, I came out to do one, so let's honor Cory with this performance."
Morrison, 34, then dedicated "What I Did for Love" from the Broadway musical "A Chorus Line" to his fallen co-star.
"He was very emotional on stage," the source told UsMagazine.com about Morrison. "It was difficult for him to get up to perform, but he did not want to disappoint anyone."