Methodist Hospital issued a statement Thursday saying the 88-year-old Bush has been in and out of the hospital recently for complications resulting from bronchitis.
The hospital says Bush is in stable condition and is expected to be released within 72 hours.
Bush's chief of staff, Jean Becker, told the Houston Chronicle the illness was not life-threatening but there had been concerns it could have developed into pneumonia.
Becker's office referred questions from The Associated Press to Bush's spokesman, who did not immediately respond to phone messages.
Bush's son, former President George W. Bush, has been among his visitors.
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