Taylor, who was 79, entered Cedars-Sinai Medical Center in Los Angeles six weeks ago for treatment of congestive heart failure, her family said.
Reynolds' husband, singer Eddie Fisher, left her for Taylor and became one of Taylor's seven husbands in 1959, but they divorced in 1964. Fisher died last year.
Taylor was single at the time of her death.
People.com said Reynolds told TV's "Access Hollywood" she and Taylor had buried the hatchet in recent years and last spoke two weeks ago.
"I said, 'Getting old is really [expletive,]'" Reynolds told the program. "And she said: 'It certainly is. It certainly is, Debbie. This is really tough.' I said, 'Well, you just hang in there now, Elizabeth.' And she said, 'I'm really trying.'
"God bless her, she's on to a better place," Reynolds, said. "I'm happy that she's out of her pain because she was in a lot of pain."