"I think the chances are better than 50-50 that he runs"

The message from Mr. Bush’s inner circle during the past few months is in part an effort to bat down speculation that the former Florida governor has ruled out a 2016 run, say GOP donors and strategists who have spoken with the Bush camp. The message, as one put it, is: “Before you do anything, let us know.”

Jim Nicholson, a Bush supporter who served in President George W. Bush’s cabinet, said: “I think the chances are better than 50-50 that he runs, and that is based on some conversations I’ve had with members of the Bush family.”

Mr. Bush’s aides aren’t actively making calls but responding to supporters who are fielding inquiries from other potential candidates, according to those involved in the conversations.