The former Massachusetts governor ventured onto the turf of a rival, Texas Gov. Rick Perry, to meet with Bush and his wife, Barbara, in the living room of their Houston home.
Romney spokeswoman Gail Gitcho said Romney and the nation's 41st president are friends, but added that the visit doesn't mean Bush will endorse Romney.
Bush spokesman Jim McGrath said the meeting was a courtesy visit, noting that Bush has met with other GOP presidential hopefuls, including Jon Huntsman.
Bush endorsed Perry during a tight race for lieutenant governor in 1998, giving Perry a winning boost.
Bush's son George won the governor's race that year.
