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As the guessing game over Sarah Palin's potential 2012 White House run continues, the former Republican vice presidential nominee kicked it up a notch Tuesday with her arrival in New York, where she hit the town with flamboyant real estate mogul Donald Trump.

"What do we have in common? A love for this country and a desire to see our economy put back on the right track," said Palin.

The presidential buzz around Palin is growing fast, thanks in large part to her recent East Coast bus tour, which greatly resembles a campaign tour. She took in Philadelphia's sites on Tuesday and is expected to visit the Statue of Liberty and Ellis Island on Wednesday.

Palin said she has not decided whether to run for president and Trump said she did not seek his support for a possible presidential campaign.

"She didn't ask me, but I will tell you she is a great woman -- a terrific woman -- and a good friend," said Trump.

He also said he'd love to see her campaigning for the White House.

"I'd love for her to run," said Trump.

Even though Trump ultimately decided against a presidential bid earlier this month, Palin says they both like the idea of a crowded Republican field.

"We both agree that competition is good and the more folks in that primary, the better," she said.

Palin was surrounded by reporters on her brief walk to a waiting limo by the Trump Tower, but she managed to squeeze in a little bit of classic campaigning by posing for a photo with a young fan.

Trump said they were just heading out for a low-key pizza dinner by Times Square. But given the presidential speculation now swirling around Palin, her visit to New York could hardly be described as "low-key."