Why not? The Republican nomination will be a wide-open affair, and more than one of the runner-up contenders from 2008 will return for another shot at the title.  And Rudy Giuliani apparently thinks he’s found a niche all to himself:

Confident that he’d have a chance to win, Rudy Giuliani is rounding up his top political advisers for a possible 2012 presidential run, sources tell Page Six.

Sources say the tough-talking former mayor “thinks the Republican race will be populated with far-right candidates like Mitt Romney, Sarah Palin and Mike Huckabee, and there’s opportunity for a moderate candidate with a background in national security.”

Giuliani has even scheduled a trip to New Hampshire for next month to meet with constituents in the state that failed him in January 2008, when he placed fourth in the Republican presidential primary.

According to the New York Post, though, even his own advisers think this is “crazy”:

The problem is that even Rudy loyalists think it’s a bad idea. “They think this is crazy,” a source said. “They realize how long the odds are, but they are standing by.”

The Post’s sources float a number of possibilities for Rudy’s interest in another primary run: bigger speaking fees, a desire to remain relevant and feed his ego, or possibly a Cabinet-level appointment in the next Republican administration.  Giuliani’s spokesperson denied that his speaking fees have declined and noted that Giuliani has traveled extensively in just the past six weeks for speaking engagements in France and Colombia, to name a couple of examples.

Perhaps the simpler explanation is that Giuliani just wants to be President.  The question will be whether his moment for that passed.  Giuliani had significant trouble convincing social conservatives to support him in 2008, but he attracted a strong following for his record of executive excellence.  Unfortunately, that record got somewhat tarnished in the 2008 primaries when his unusual campaign strategy left him far out of the running in the early primaries and his big gamble on Florida failed to pay off.  Giuliani will have to overcome the same concerns over his approach to social issues that he did in 2008, and would also have to address a lack of confidence in his ability to run a successful campaign.

Times have also changed around Giuliani.  In 2008, with Barack Obama ascending and the nation deep in Bush fatigue, a centrist or center-right candidate seemed like the right prescription for the uphill GOP slog.  The collapse of support for Democrats after their two years in absolute control in Washington has changed that calculus.  The broad midterm victory showed that fiscal conservatism will matter most to voters, but that it doesn’t necessarily take a centrist or an establishment candidate to sell it.  Marco Rubio blew the  doors off of the election in Florida by fighting both parties to victory on the basis of strong fiscal conservatism and support for pro-life positions.  Clearly, the ground has changed considerably since Rudy’s 2008 run, and not necessarily in his favor.

Still, don’t count him out entirely.  Giuliani beat the Mob, and he beat Democrats in the Big Apple to win two terms as mayor of the nation’s largest city.  He’s used to long odds. Rudy’s presence in a presidential primary race will provide more focus on national security, and that won’t be a bad idea at all.