"He retired from presidential politics many years ago," said the spokesman, who did not wish to be named.
The announcement came a day after Bush's vice president, Dick Cheney, announced he would cross party lines and vote for Democratic presidential candidate Kamala Harris over Republican former President Donald Trump.
Cheney, who served as vice president under Bush from 2001 to 2009, said on Friday that "in our nation's 248-year history, there has never been an individual who is a greater threat to our republic than Donald Trump."
Harris said on Saturday endorsements of her by Dick Cheney and his daughter Liz, a former US Representative, were "courageous" for putting country ahead of political party.
Mike Pence, who served as Trump's vice president for four years, has said he will not endorse his former boss but has not backed Harris.
