Family spokesman Jim McGrath said in a statement that the Bushes thank everyone for their prayers and good wishes. The 88-year-old is said to be alert and in good spirits. In fact, his conversations with doctors and nurses now include singing.
Physicians remain optimistic about his current course of treatment.
Bush has been hospitalized since Nov. 23. He was moved to intensive care Sunday to be treated for a fever following a bronchitis-related cough.
Bush, also a former U.S. ambassador to China and CIA director, suffers from a form of Parkinson's disease that forced him in recent years to use a motorized scooter or wheelchair for mobility.
The 41st president, is the country's oldest living former president by a few months.
The Associated Press contributed to this report.
