Mr Bush's chief of staff, Jean Becker, says the 88-year-old is being treated for bronchitis at Houston's Methodist Hospital. She says he was admitted last Friday and is expected to be released by the weekend.
Ms Becker told the Houston Chronicle that the illness was not life-threatening but there had been concerns it could have developed into pneumonia.
Mr Bush's son, former president George W Bush, has been among visitors.
The senior Bush was president from 1988 to 1992 and vice-president to Ronald Reagan.