Miss Lee, 78, is best known for her rendition of Fever and in 1969 won a Grammy for best contemporary female vocal performance for the hit Is That All There Is?
Her daughter Nicki Lee Foster said: "She's conscious and her family has been with her."
Ms Foster said doctors were trying to determine whether the stroke, which the singer suffered on 27 October, had caused permanent damage.
A diabetic, Miss Lee has suffered a string of health problems including a near-fatal fall in a New York hotel in 1976.
She was seriously injured in a Las Vegas fall in 1987 and in early 1985, she had surgery to open clogged arteries. Later that year, she underwent double-bypass heart surgery.
Ms Foster declined to say where her mother was being treated.
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Loving-Lee: A Peggy Lee fan page
Peggy Lee fan page
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