Mayor Giuliani’s decision to skip a high-profile showcase for potential Republican presidential candidates this weekend is drawing quizzical reactions from some strategists and fueling debate about whether he is serious about seeking the presidency in 2008.

The list of speakers for the Memphis gathering contains almost all the top prospects for the Republican nomination, including the local favorite, Majority Leader Frist, as well as Governor Romney of Massachusetts, and Senators Allen of Virginia, Brownback of Kansas, and McCain of Arizona.

To stoke the presidential embers further, the conference and a leading political newsletter will conduct a straw poll at the event to gauge how the potential candidates are faring at winning support from Republican activists and local officials.

A spokesman for the Southern Republican Leadership Conference, Kevin Phillips, told The New York Sun that his group extended an invitation to Mr. Giuliani but he indicated he did not plan to attend.

“It was recently, sort of, politely declined,” Mr. Phillips said.

A former parks commissioner under Mr. Giuliani, Henry Stern, said in an interview yesterday that he doesn’t see any indication that the former mayor is readying a presidential bid.

“He campaigns for Republican candidates and has given money and so on, but hasn’t made the all-consuming effort that is usually required for the presidency track,” Mr. Stern said. “There’s no visible sign of deploying operatives to other states, building a personal organization.”

Mr. Stern, who said he has not spoken to Mr. Giuliani about his intentions, said the former mayor is focused intently on the economic pursuits of his consulting and investment-banking firm, Giuliani Partners. “He is, it seems, keeping his options open, making money. He seems more concerned with his business,” Mr. Stern said.

Mr. Giuliani’s spokeswoman, Sunny Mindel, did not return calls yesterday seeking comment for this story.

At a speech to a jewelry show in Manhattan on Sunday, Mr. Giuliani said it was too soon to talk about whether he will run for the presidency in 2008, according to a report on an industry Web site, Diamonds.net.

“Ask me again in one year,” the former mayor was quoted as saying.

A history professor who occasionally wrote speeches for Mr. Giuliani in the 1990s, Fred Siegel, said yesterday that the former mayor’s decision to dispense with the usual trappings of a presidential proto-campaign should not be seen as an indication that he will not run in 2008.

“I don’t think it’s that he’s not running. It’s that he’s not running in any conventional sense,” said Mr. Siegel, who teaches at Cooper Union and recently published a book entitled, “Prince of the City: Giuliani, New York, and the Genius of American Life.” “He’s running an unconventional campaign but he’s running,” the professor said.

“He talks to business groups. He talks to motivational groups, but he’s not on the rubber-chicken circuit,” Mr. Siegel said, referring to the seemingly endless series of local political party dinners frequented by most presidential hopefuls.

One reason for Mr. Giuliani to avoid gatherings of hard-core Republican faithful is that he does not appeal as strongly to those activists as candidates with more conservative social views.

“This is a smart move for him. He can’t win on conventional terms,” Mr. Siegel said. He said plans to compress the line up of early primary states, deemphasizing states such as Iowa and New Hampshire, could boost Mr. Giuliani’s ability to mount a late-starting, centrist bid for the nomination. A poor showing by GOP Congressional candidates in November could also strengthen Mr. Giuliani’s hand.

Mr. Stern indicated yesterday that Mr. Giuliani’s decision to hang back might not be the best way for him to advance his prospects if he is serious about running in 2008. “Every day that the hare rests, the tortoise gains an advantage,” Mr. Stern warned.

One national political analyst, Chuck Todd, said yesterday that Mr. Giuliani’s decision to skip the gathering of Southern Republicans makes little sense if he is serious about running.

“Notice McCain is not skipping it. McCain knows the work he needs to do and he’s not ever going to insult them at any point in time,” said Mr. Todd, editor-in-chief of the political newsletter sponsoring the straw poll, the Hotline.

Mr. Todd said he does not put much faith in poll numbers showing Mr. Giuliani to be the most popular potential candidate in either party. “Those numbers drop dramatically the day he announces,” the editor said. He said most voters don’t know about Mr. Giuliani’s support for abortion rights and gay rights.

Mr. Todd said he does not believe Mr. Giuliani will ever launch a formal bid for the presidency. “I’ve always assumed he is using the presidential rumors to make money,” Mr. Todd said.

While Mr. Giuliani’s absence from the so-called “cattle call” in Tennessee is the most notable, another possible contender for the Republican nomination is also staying away: Governor Pataki. He is limiting his travel after being discharged from hospital yesterday following a three-week stay for intestinal problems that followed appendicitis.

Mr. Giuliani’s plan to bypass the Tennessee gathering was first reported by Newsweek.