George Kovacik, a spokesman for Methodist Hospital, said Sunday there has been no change over the last couple of days in the status of the 88-year-old Bush.
Aides originally said the 41st president could be released from the hospital this weekend. But his cough has yet to clear up, meaning he has stayed put while doctors "play it safe."
Bush has been in and out of the hospital recently for complications resulting from bronchitis.
Hospital visitors have included Bush's son, former President George W. Bush, and his wife, former first lady Laura Bush. They live in Dallas.