McGrath said physicians want the cough to go away completely before Bush is discharged.
"They don't want to put him through this again," McGrath said.
Bush's son, former President George W. Bush, and his wife, former first lady Laura Bush, slipped in to see him Sunday. They now live in Dallas.
The elder Bush was vice president under Ronald Reagan from 1980 to 1988, when he was elected president. He lost his re-election bid to Bill Clinton four years later.
Bush and his wife, Barbara, now make their winter home in Houston and spend summers in Kennebunkport, Maine.
Bush was seen a few weeks ago attending a Houston Texans NFL game, something he does frequently. He suffers a form of Parkinson's disease that has forced him to use a wheelchair or motorized scooter to get around.
The former president was a naval aviator in World War II — at one point the youngest in the Navy — and was shot down over the Pacific. He achieved notoriety in retirement for skydiving on at least three of his birthdays since leaving the White House in 1992.