The retired politician, 88, has been receiving treatment at the Methodist Hospital in Houston, Texas for the past few days after experiencing a lingering cough.
His Chief-of-Staff, Jean Becker, reveals Bush Sr. has been in and out of hospital in recent weeks, but his family hopes to have the patriarch discharged by this weekend (01-02Dec12).
Becker tells local publication the Houston Chronicle, "His big problem is a chronic cough, he can't get rid of so he's back at Methodist. This is not a life-threatening illness."
She adds that initial fears the World War II veteran, who has been suffering from a form of Parkinson's disease, would develop pneumonia have proved unfounded.
Bush Sr. served as U.S. leader from 1989 to 1993.