NEW YORK (CNN/Money) - Halliburton Co., which has already won the job of fixing Iraq's oil fields after the war, could also get a piece of the action in rebuilding the country's infrastructure, though its potential role is still unclear.

Last week, news reports said Halliburton, once headed by Vice President Dick Cheney, was not in the running to get a State Department contract worth up to $600 million to rebuild Iraq's roads, bridges, hospitals and schools and do other jobs necessary to help 24 million Iraqis get back to something approaching a normal life.

But a Wall Street Journal report this week said KBR might already be in line as a subcontractor to Parsons Corp., a private construction company based in Pasadena, Calif., reportedly one of the two finalists for the contract, which could be awarded as early as next week.

Without commenting on any potential arrangements with Parsons or San Francisco-based Bechtel Corp., the other reported finalist, Halliburton admits its Kellogg Brown & Root (KBR) construction unit could take part in the reconstruction effort.

"KBR remains a potential subcontractor for this important work," Halliburton spokeswoman Wendy Hall said.

Parsons, Bechtel and the U.S. Agency for International Development (USAID), the State Department arm administering the contracts, declined to comment.

KBR, which handles general construction work in addition to more specialized work building oil rigs and pipelines, has already won the job of doing emergency repairs to Iraq's oil infrastructure. That job will be done on a "cost-plus" basis, meaning KBR will be paid for the costs of doing the work, plus a fee that represents a set percentage of those costs.

President Bush, as part of his supplemental budget request for war and short-term rebuilding costs, asked for nearly $500 million for oilfield repair, meaning KBR's contract could be almost as lucrative as the entire USAID rebuilding contract.

It's unclear why KBR dropped out of the running for the rebuilding contract. It's possible the USAID felt KBR's bid wasn't competitive enough.

But KBR might have withdrawn its bid because of fear of political backlash. Watchdog groups and Representative Henry Waxman, D-Calif., protested when Halliburton won the Army contract, in part because there were no bids taken on the job, and documentation of the contract was unavailable to the public.

Some analysts have pointed out that Houston-based Halliburton, the world's largest oilfield services company, has business elsewhere in the region and might not want to be seen as reaping any spoils from its prior relationship with Vice President Cheney.

"Obviously, politics is probably more of a negative than a positive for Halliburton, which is unfortunate because it is the most qualified company in the world, in my opinion, to do a lot of the work," said Gary Russell, an analyst at Stifel Nicolaus & Co., an investment banking firm in St. Louis.

Cheney, who was CEO of the company from 1995 to 2000, divested himself of most of his interest in Halliburton before the 2000 presidential election. He still has stock options, but has promised to donate any profits from those options to charity. He also receives deferred compensation from the company, but is guaranteed to get that money even if Halliburton goes bankrupt.

It's unclear just how much of the general contracting work Halliburton might get as a subcontractor. When Parsons won a contract from USAID to rebuild post-war Kosovo in the late 1990s, it was required to subcontract the vast majority of that work to Bosnian construction companies.

Halliburton did get a small job from the government, supporting U.S. peacekeeping forces with food, laundry, transportation and other services in Bosnia, Croatia and Hungary.

Such work makes up only a fraction of Halliburton's total business -- possibly less than a quarter of its engineering unit's $5.7 billion annual revenue -- and a small portion of a $600 million contract might not make much of a difference to its bottom line.

But future building projects, which might be administered by a new Iraqi government unconcerned about the reactions of the media or California Democrats, could be worth billions of dollars, and Halliburton is well-positioned to take advantage.

"The range of possibilities is still pretty vast," said Russell, who personally owns no Halliburton (HAL: up $0.04 to $20.64, Research, Estimates) shares and has a $28 price target and a "buy" rating on the stock. "Future projects, if they get into the hundreds of millions of dollars, could be impactive to earnings."