Former New York City Mayor Rudy Giuliani (R) said he is "absolutely" open to a run for president in 2012.

Giuliani, the mayor of New York during the 9/11 terrorist attacks who ran for president in 2008, hinted more strongly that he might seek the Republican nomination to challenge President Obama's reelection.

"I will take a look at 2012. It's really a question of, can I play a useful role? Would I have a chance of getting the nomination? Those are things that I'll have to evaluate as the year goes along," Giuliani said Thursday night on CNBC's "The Kudlow Report."

The New York Post had reported earlier this month that Giuliani was looking to round up staff to prepare a possible presidential bid in 2012. But the former mayor denied it.

He ran in 2008 for the Republican nomination, and had enjoyed frontrunner status for a number of months heading into the thick of the primary. But Giuliani eventually lost key primary races to other GOP candidates, prompting him to withdraw and endorse Sen. John McCain (R-Ariz.).

Asked if the door to a 2012 run were open, Giuliani said: "Yes, yes, absolutely."