Another Bush may be making a run for the Oval Office. Jeb Bush, the former governor of Florida, son of President George H.W. Bush and brother of President George W. Bush, is leaning toward a 2016 campaign for the presidency, the New York Times reported.

Advisers of the 61-year-old politician have begun building a staff to make a push during the primary-election season, the Times said. Bushs previous concerns about a presidential run are starting to subside, the newspaper said, citing his friends and supporters.

“It’s now about a realistic assessment of whether the journey he wants to travel is compatible with winning a primary,” Al Cardenas, a friend and the chairman of the Florida Republican Party during Bush’s governorship, told the New York Times.

The Times report suggested Bush could run as a centrist in a primary-election field currently featuring mostly far-right potential candidates. “I just said to him, ‘I think if you look back, despite the far right’s complaints, it is the centrist that wins the nomination,’” U.S. Sen. John McCain, R-Ariz, reportedly advised Bush in a meeting this fall.

Although Bush has conservative positions on issues such as abortion and taxes, he has exhibited a willingness to reach across the political aisle at times, advocating for bipartisan consensus when it comes to fiscal issues and immigration, which many other GOP politicians reject.

A Bush win could have profound implications for the Republican Party and the direction it would go during the next presidential term, depending on the kind of campaign he decides to run. A right-center approach runs the risk of losing primary-voter support, which, in turn, could imply the Republican Party is no longer interested in candidates who veer closer to the center than to the right.