"President Bush's breathing has returned to normal, but he will remain at the Houston Methodist Hospital tonight (Monday night) pending final approval from his doctors to return home," a statement from his office said.
On behalf of both the President and Mrs Bush, the statement thanked everyone for their good wishes and prayers.
The 41st President spent last week at the hospital after experiencing shortness of breath on December 23. A spokesman said the stay was just a precaution for the 90-year-old.
Bush enjoyed watching football with his wife and sent his congratulations to the hometown team, he said.
"President and Mrs Bush enjoyed watching the Houston Texans football game together today, and send their congratulations to Coach Bill O'Brien and the team for a hard- fought, winning season," he added.
The oldest of the four living former US presidents, Senior Bush, who uses a wheelchair, appeared frail in recent public appearances.
The statement further said the news of his possible discharge would be conveyed soon. Bush, patriarch of one of America's most prominent political dynasties, is father to the 43rd president George W Bush.
Another son, Jeb Bush, last week announced his aim laying the foundation for his own 2016 White House bid.