Texas' longest-serving governor, Perry took office in 2000 when President-elect George W. Bush resigned, and won a third full term last November. Rush Limbaugh is among the conservative leaders who've floated his name in recent weeks.
At a press conference in Austin, he was asked if he'd think about running when the Texas Legislature adjourns on Monday.
"Yes sir. I’m going to think about it," he said, according to the Houston Chronicle. But he added: "I think about a lot of things."
Perry, who serves as chairman of the Republican Governors Assn., has stepped up his national profile in recent years. He has embraced the "tea party" movement, and championed 10th Amendment rights for state governments.
But at home, he's been faced with a budget deficit in the tens of billions. The state appears set to approve a final budget that balances its books by slashing public education and other government spending.
When he embarked on a national book tour earlier this year, Perry repeatedly denied that he would run for president. In an interview just this week on Fox News Channel, he said to Greta Van Susteren that he's "tempted" to run, but, "the fact is: this is something I don't want to do."
"My hope is that that person will come forward that can win the presidency that we can all get behind," he said then.
Indiana Gov. Mitch Daniels' decision Sunday to get out of the race seems to have opened led both newcomers and familiar names to at least give the race a look.
Michigan Rep. Thaddeus McCotter is planning a visit to all-important New Hampshire. Former New York Gov. George Pataki, who had ruled out a run, says he's reconsidering. And Rudy Giuliani, whose run as "America's Mayor" in 2008 sputtered with a failed Florida strategy, is making noises about giving it another shot in 2012.
Then, of course, there's Sarah Palin, who jolted the field Thursday with her announcement of a national bus tour that is either the warm-up to a candidacy or a headline-grabbing self-promotional effort that will distract attention from the field of actual candidates, depending on whom you ask.
Though there is a series of debates scheduled this summer, including one in New Hampshire in June, there's no real legal deadline looming for months for candidates interested in running. But in modern history no candidate has gotten in later than Memorial Day and run a successful campaign.
A new CNN/Opinion Research poll released Friday showed Giuliani, who has yet to make any overt moves, actually leads the field with 16% of the vote, followed by Mitt Romney at 15%, and Sarah Palin at 13%. Ron Paul and Herman Cain round out the top five, all in double-digits.