Moore, 49, is reportedly seeking treatment for substance abuse and an eating disorder at the facility, which in the past has reportedly played host to such high-profile patients as Eva Mendes and Lindsay Lohan.
Mueller has reportedly been seeking treatment for cocaine addiction at Cirque Lodge.
However, a source tells the web site that Moore, 49, has not crossed paths with Mueller -- or anyone else there, for that matter --because she's still in the early stages of her treatment.
"She hasn't had any interaction with other patients yet," the source said. "She is still in detox at the moment."
Moore was hospitalized on January 23, after emergency workers responded to a 911 call that was placed at 10:45 p.m. TMZ reported that a friend of Moore's told paramedics she had over-indulged in nitrous oxide -- also referred to as whip-its -- though in the 911 call a woman told the dispatcher that the actress had smoked something. According to the caller, the substance wan't marijuana, but something similar to incense.
Following Moore's hospitalization, her representative told TheWrap that the actress would seek treatment for "exhaustion," citing "the stresses in her life right now.
"Because of the stresses in her life right now, Demi has chosen to seek professional assistance to treat her exhaustion and improve her overall health," the representative said. "She looks forward to getting well and is grateful for the support of her family and friends."
Moore's hospitalization came shortly after her November 2011 announcement that she was divorcing her husband of six years, Ashton Kutcher, after six years of marriage amid reports that Kutcher had cheated on Moore.
"here are certain values and vows that I hold sacred," Moore said in the statement announcing the divorce.
