"President Bush's condition has improved to the point that doctors have begun discussing dates for his discharge. He will remain at the Houston Methodist Hospital through the weekend for further observation," Bush's spokesman Jim McGrath said in a statement.
Bush, 90, who is the oldest living former US president was taken to the hospital Tuesday night as a precautionary measure after experiencing shortness of breath.
On Christmas Day, he received visits from his wife, Barbara, son Neil and daughter-in-law Maria Bush, McGrath had said earlier.
The latest health scare comes two years after Bush, who was president from 1989 to 1993, was admitted to the same hospital for treatment of bronchitis and related ailments.
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Bush spent seven weeks recuperating and became so ill he was believed at one point to be near death.
The former Republican president suffers from Parkinson's disease and cannot use his legs.
But he celebrated his 90th birthday on June 12 by skydiving in Kennebunkport, Maine, with the Army's Golden Knight parachute team.