Close aides and friends say he is actively weighing a run, something he didn’t do in the last election cycle. “Gov. Bush has made a decision to make a decision at some point about running for president,” said Sally Bradshaw, a longtime adviser who talks frequently with Mr. Bush, who declined to comment for this article…

But conservatives worry about leaning on the Bush name yet again at a time when the GOP is trying to reintroduce itself to voters and can draw on plenty of new talents, including Florida senator and Bush protégé Marco Rubio, Louisiana Gov. Bobby Jindal and New Jersey Gov. Chris Christie. No Republican not named Bush has won the White House since 1984, an eternity in politics.

Murmurings about a possible Bush run have already provoked groans in some quarters. It is time for conservatives “to move beyond picking the next elder white guy in line,” said Matt Kibbe, a prominent tea-party activist and president of FreedomWorks, a conservative campaign group.