The 84-year-old had been rushed to hospital in "fair to serious condition," paramedics told AFP, after collapsing at the Beverly Hills home of her son Todd Fisher around 1.00 pm (2100 GMT).
"She wanted to be with Carrie," he was quoted as telling industry weekly Variety magazine.
Celebrity news portal TMZ said Reynolds had died "as a result of a stroke," also citing her son.
Fisher, who catapulted to worldwide stardom as rebel warrior Princess Leia in the original "Star Wars" trilogy, died in Los Angeles on Tuesday, four days after suffering a heart attack on a transatlantic flight.
TMZ, citing unnamed family sources, said Reynolds had been at her son's house to discuss funeral arrangements when she became ill.
"Thank you to everyone who has embraced the gifts and talents of my beloved and amazing daughter," she posted on Facebook following her daughter's death.
"I am grateful for your thoughts and prayers that are now guiding her to her next stop."
Reynolds, who received the Academy's Jean Hersholt Humanitarian Award last year, first captivated audiences in 1952's "Singin' in the Rain."
She was later nominated for an Oscar and helped found a group that works to combat mental health issues.
Her 2013 autobiography "Unsinkable: A Memoir" detailed the highs and lows of her rocky personal life and a screen career forged in the glamour of Hollywood's "Golden Age" which was still going well into the 1990s.
Known at one time as the foremost collector of Hollywood memorabilia, Reynolds married singer Eddie Fisher in 1955 and had two children, Carrie and Todd. The couple divorced in 1959 after he fell for Elizabeth Taylor.
Born Mary Frances Reynolds on April 1, 1932 in El Paso, Texas, the second child of railroad carpenter Raymond Francis Reynolds and his wife Maxine, she came to the notice of Hollywood studio MGM after winning a California beauty contest at age 16.
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