A criminal investigation is under way after a hacker apparently accessed private photos and emails sent between members of the Bush family, including both former presidents.
The 88-year-old was discharged from hospital last month after treatment for bronchitis.
Bush spokesman Jim McGrath told the Houston Chronicle the matter is "under criminal investigation".
The Smoking Gun says the hacker went by the online moniker Guccifer, a word plastered across the leaked photos in translucent, neon blue print.
The website quotes Guccifer as describing himself as a veteran hacker who has long been in the government's sights.
The website displayed photos it said came from the hacker, including one that purported to show the elder Bush during his recent near-two-month stay in a Houston hospital.
The authenticity of the photos and other details on the website could not immediately be confirmed.
The FBI in Houston was tight-lipped. "We do not confirm or deny the existence of any investigation," said a spokeswoman.