A statement issued on behalf of Coleen, her husband, Manchester United star Wayne, and the rest of Rosie's family, said: "Sadly our special angel Rosie, our much-loved daughter and sister, went to heaven at 2.50am this morning at home, where she was surrounded by her loving family.
"Rosie was just 14 years old, and fought a life-long battle with Rett syndrome. Throughout her life she brought so much love and happiness to all our family and everyone who knew and met her.
"She was such a strong little girl and an inspiration to us all. We shall cherish forever the memories we have shared and the love she showed us each and every day of her life.
"As a family we are heartbroken, but we are blessed to have had her in our lives.
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Greater Manchester Police said "inquiries are ongoing to fully understand the circumstances of the incident."
Business Secretary Greg Clark said talks with Peugeot's boss over a potential Vauxhall takeover were both "constructive and reassuring".
He served in Margaret Thatcher's Cabinet as Home Secretary in 1989 and was also a former Governor of Bermuda.