While actor-turned-politician Fred Thompson’s (R) public flirtation with a 2008 presidential bid has garnered increasing media attention, behind the headlines lie a litany of logistical questions about the former Tennessee Senator’s ability to build a campaign operation should he decide to run.

Those close to Thompson say his interest in a White House run is genuine. Yet the practical evidence that he is preparing to build a national political and fundraising team from scratch — at a point when his GOP competitors are already well out of the gate — remains minimal.

Thompson is taking counsel from former Senate Majority Leaders Howard Baker (R-Tenn.) and Bill Frist (R-Tenn.) as well as from Sen. Lamar Alexander (R-Tenn.), and several House Republicans are also wooing him to run. But the star of NBC’s “Law & Order,” whose last political campaign was in 1996, has no ready-made political organization of his own.

If he runs, he is expected to borrow some from Frist’s inner circle of political advisers.

Frist was preparing a presidential bid but announced late last year that he would not run, leaving his would-be campaign team without a horse in the 2008 contest. By and large, those advisers have not jumped to other campaigns and their ties to Tennessee and a national fundraising network would be a natural starting point for getting a Thompson operation off the ground.

“I think it is a good assumption that a significant piece of team Frist would be involved with Fred should he decide to run,” said one former Frist operative who is talking to Thompson.

Among those in Frist’s brain trust who could be involved are lobbyist Alex Vogel, a former counsel to Frist, fundraiser Linus Catignani, the former Majority Leader’s top money man, and Eric Ueland, a former Frist chief of staff. Vogel and Catignani worked for the National Republican Senatorial Committee during Frist’s tenure as chairman in the 2002 cycle.

But several other Frist operatives aren’t available, including Chip Saltzman, who is now managing former Arkansas Gov. Mike Huckabee’s (R) long shot White House bid.

Tennessee Republican Party Chairman Bob Davis, a former top Senate aide to Thompson, and Mark Corallo, who is serving as spokesman, have taken the most public role thus far in Thompson’s exploratory effort.

Corallo worked for the House Government Reform Committee in the late 1990s and later as a spokesman for the Department of Justice. Thompson served as chairman of the Governmental Affairs panel in the Senate, and led the investigation into allegations of Democratic fundraising abuses connected to China in the 1996 White House campaign.

Behind the scenes, former House Government Reform investigator David Bossie — best known for his attacks on President Bill Clinton and now-Sen. Hillary Rodham Clinton (D-N.Y.) — and Ed McFadden, a former Justice employee, also are involved in the Thompson effort.

But one Republican strategist who is not aligned with any of the 2008 presidential campaigns, said that the lack of organization by Thompson thus far is doing little to harness the enthusiasm that the idea of his candidacy has generated.

“No one knows who to talk to,” the operative said. “They are not doing anything that would indicate they are serious about running.”

The timing of Thompson’s decision will have a major impact on his campaign, should it materialize, with some observers suggesting that he may wait as late as Labor Day to decide if he will run.

“I think he’s seriously interested,” said Alexander, who succeeded Thompson in the Senate and twice launched unsuccessful presidential bids. “He has a unique and commanding presence, maybe the only one I can think of who could enter the race in the fall.”

Alexander’s chief of staff Tom Ingram, a longtime Tennessee political operative, also has talked to Thompson. Ingram took a leave of absence last fall to run the campaign of now-Sen. Bob Corker (R-Tenn.). He also managed Alexander’s campaign and worked on Thompson’s 1996 re-election.

While Thompson’s Hollywood persona gives him more leeway than most presidential hopefuls, the later he waits to get in the bigger the logistical challenges of putting together a structurally sound campaign will be.

Although there are still some bodies left in the pool of political talent who are uncommitted in 2008, that isn’t likely to be the case come fall.

“Everybody’s pretty much got their main people in place,” said another seasoned GOP operative who is not working for any presidential contender. “Inevitably, one campaign is going to clean house at some point.”

Beyond just putting together a political team, Thompson also would need to get into the fundraising game soon in order to have the opportunity to scoop up big donors who are not yet committed to other candidates.

As far as consultants go, even now the pickings are somewhat slim.

GOP media consultant Alex Castellanos, who did the media for Thompson’s last campaign in 1996, is working for former Massachusetts Gov. Mitt Romney (R).

Fred Davis, another well-known Republican ad man who worked on Corker’s campaign in Tennessee last cycle, is on board with Sen. John McCain (R-Ariz.) for 2008. Both Castellanos and Davis have worked for President Bush and on California Gov. Arnold Schwarzenegger’s (R) 2006 re-election. Schwarzenegger, like Thompson, parlayed a Hollywood acting career into a successful run for elected office.

After leaving the Senate in 2002, Thompson resumed his acting career and currently plays Manhattan District Attorney Arthur Branch on “Law & Order.”

Meanwhile, aside from Frist’s team, Thompson also could look to the remnants of former Sen. George Allen’s (R-Va.) intended 2008 campaign.

Allen lost his re-election bid last year and his political operation has largely disbanded.

His media consultant, Scott Howell of Scott Howell & Company, currently is unaffiliated with any of the other 2008 GOP presidential contenders.

Former Republican National Committee Chairman Ed Gillespie, who was treasurer of Allen’s political action committee and expected to play a role in his White House campaign, was seen having lunch with Thompson last week.

Gillespie is now chairman of the Republican Party of Virginia.

John Stanton and Josh Kurtz contributed to this report.