While many of the Republican candidates for president are scrambling to cast themselves as the next Ronald Reagan, Mayor Bloomberg this week will be entertaining the wife of the deceased 40th president, Nancy Reagan, at his Upper East Side townhouse, as well as hosting a fund-raiser for the Ronald Reagan Presidential Library.

Political analysts say any link between Mr. Bloomberg and Reagan would be a boost for the mayor if he ran for president as a third-party candidate. Reagan’s name is invoked repeatedly on the Republican campaign trail, and candidates tried to tie themselves to his legacy at nearly every opportunity during the first Republican debate, held in May at the Reagan Library in Simi Valley, Calif.

“If Bloomberg does decide to run, his only real chance of winning is to attract people from across the spectrum,” the director of the University of Virginia’s Center for Politics, Larry Sabato, said. “This certainly is one way to get the attention of Republicans. There are going to be a certain number of Republicans disgruntled with the nominee, no matter who it is.”

Talk of Mr. Bloomberg as a possible presidential candidate has soared in the past week, after the mayor appeared on the cover of Newsweek as the subject of an article that framed him as a national candidate. Mr. Bloomberg’s chief political adviser, Kevin Sheekey, told the magazine Mr. Bloomberg would run a billion-dollar campaign if he ran for president.

In June, Mr. Bloomberg left the Republican Party, fueling speculation that he was laying the groundwork for a third-party White House run. He had been a lifelong Democrat, but switched parties before he ran for mayor in 2001.

A Democratic pollster, Peter Hart, said voters are looking for a candidate who can reduce partisan fighting in government, curtail the influence of special interest groups, make government more active in health and safety matters, and bring a sense of optimism to the country.

Mr. Hart said Mr. Bloomberg is in a unique position to draw from the legacies of Reagan and President Clinton to show he represents something different.

“That avenue is open to someone who is an outsider and not part of the process,” he said. Mr. Hart added that by hosting the Reagan Library fund-raiser, Mr. Bloomberg is saying he is going to pick and choose the best elements from all sides.

One central policy area on which Mr. Bloomberg and Mrs. Reagan share common views is support for stem cell research.

In 2006, Mr. Bloomberg donated $100 million to his alma mater, Johns Hopkins University, a substantial part of which was to fund stem cell research, according to a Reuters report that cited an unnamed source.

After Reagan developed Alzheimer’s disease, Mrs. Reagan became a proponent for stem cell research, which has been opposed by many conservatives, including President Bush, because it involves the destruction of human embryos.

The dean of Baruch College’s school of public affairs, David Birdsell, said it’s unclear whether Mr. Bloomberg’s fund-raiser for the Reagan Library is part of a “Bloomberg presidential campaign.”

Mr. Bloomberg has hosted many fund-raisers in his home, including an event in 2006 for Senator Lieberman and more recently for the president of Brooklyn, Martin Markowitz, and City Council members Simcha Felder and Peter Vallone Jr.

“What he’s doing is consistent with the activities of a prominent philanthropist,” Mr. Birdsell said. “Were he not running for president, none of this would surprise us in the least. The fact that he may be running for president, it may give him a slight advantage.”

He said the private fund-raiser allows Mr. Bloomberg to pay homage to Reagan and his presidency and associate himself in the process “with an icon of middle America.”

Mr. Birdsell said that by not publicizing the fund-raiser, Mr. Bloomberg is protecting himself from any potential backlash from Republican candidates who are seeking to be the next Reagan.

A spokesman for Mr. Bloomberg, Stuart Loeser, wrote in an e-mail message that he had no comment on the fund-raiser. The Reagan Foundation lists Mr. Bloomberg as a 2006-07 contributor on its Web site, but does not list contributors from other years.

A political consultant, Joseph Mercurio, said the fund-raiser is another example of Mr. Bloomberg adopting a schedule that would be expected from a presidential candidate.

Mr. Bloomberg is scheduled to speak at a National League of Cities convention in New Orleans on Friday and is planning to travel to the island of Bali in Indonesia to attend a United Nations summit on climate change in December. Earlier this month he announced his support for a tax on carbon emissions in Seattle.

“I think he’s smart enough to understand that if you run as an independent you have to get votes from people who are not aligned and people who are Democrats and people who are Republicans,” Mr. Mercurio said.

Hosting a fund-raiser for the Reagan Library and being photographed with Mrs. Reagan, he said, “sounds like a very good thing to be doing if you are a presidential candidate.”