After offering advice to Washington and New York reporters as to how they should best cover the 2008 presidential campaigns, the mayor went on to offer a laundry list of issues — from Iraq to Social Security to immigration — that presidential candidates should address.

His political alter-ego Kevin Sheekey was then seen taking business cards from the would-be draft leaders.

Bloomberg was in Washington Tuesday to address the Brookings Institution’s Center on Children and Families after the release of the census poverty report.

And despite the news he made with his speech, in which he said he wanted to see a dramatic expansion of the earned income tax credit, it seems the mayor can’t step foot inside the Beltway without being hounded by questions about a possible candidacy.

Despite his denials, Bloomberg continues to draw skepticism and attention from national political reporters, convinced or curious that the mayor might join forces with someone like Sen. Chuck Hagel (R-Neb.) for a third-party bid.

When asked about a dinner with Hagel that drew national media attention, Bloomberg joked that he “chose a restaurant that would be quiet, out of the way, where no one would see us.”

“It’s called The Palm,” he deadpanned.

Bloomberg said the fascination with his possible (but not-going-to-happen) presidential run stems mainly from media boredom with the current field of candidates.

“You guys have to fill inches and minutes,” he said.

But it was Strobe Talbott, president of the Brookings Institution, who first broached the subject while introducing Bloomberg.

“Whatever he decides, it is a credit to him that he would be seen as a leader of national stature,” Talbott said.

Perhaps seeing an opportunity for a joke, Bloomberg led off by addressing the Washington rumor machine.

“Despite any rumors you may have heard, I did not come to Washington as part of a stealth campaign to become the next attorney general,” Bloomberg said.

Despite all the jokes, the mayor, in a press conference after his speech, sounded a lot like a candidate as he went down the menu of issues current candidates are addressing on a daily basis.

Bloomberg talked about healthcare policies, raising the miles-per-gallon standards of American-made cars, and America’s “damaged” relationships with foreign countries.

On immigration, Bloomberg said the current policies are moving America in the wrong direction, and it will take decades to recover.

“The anti-immigration wave is the single most damaging thing taking place in this country,” he said.

On other issues, Bloomberg, who sent interest soaring when he changed his political affiliation from Republican to Independent earlier this year, said everyone, including both major political parties and both sides of Pennsylvania Avenue, are to blame for not keeping the U.S. competitive.

But when asked if he thought his anti-poverty or healthcare plans were better than any of the presidential candidates, Bloomberg demurred.

“I’m not here to preach to anybody else,” he said.