The 58-year-old daughter of jazz legend Nat King Cole entered a New York hospital Sept. 12.
O'Connor said Cole has been receiving kidney dialysis that isn't related to her struggle with hepatitis C, a liver disease spread through contact with infected blood.
Cole announced in July that she was suffering from the disease, revealed to her during a routine examination, and that it was likely caused by her drug use years ago.
At the time of Cole's hospitalization, O'Connor blamed the singer's problems on the medicine she had been taking and a busy publicity schedule to promote her new album, "Still Unforgettable."
Cole canceled her singing appearances this month. O'Connor said she did not know when she will hit the road again in support of the disc.
Cole has sold millions of albums in her own long career. Her best-selling work was her 1991 multiple-Grammy winning CD, "Unforgettable ... With Love," on which she remade some of her father's classics.