NEWARK, N.J. – Walmart Stores may spend hundreds of millions of dollars investigating $24 million in alleged Mexican bribes as the U.S. government weighs whether the company or executives also broke the law by covering up an internal probe, former federal prosecutors said.

The company said it’s aiding U.S. probes of payments detailed April 21 in the New York Times. The newspaper said Walmart de Mexico failed to fully investigate the bribe claims as well as well as $16 million in “donations” to Mexican local governments to fuel store expansion in the country up to 2005.

Walmart disclosed the payments to the Justice Department and Securities and Exchange Commission, according to a December 2011 regulatory filing, and said its outside advisers are briefing the agencies on its own probe. Prosecutors will want to know why Walmart didn’t fully examine claims in 2005 by a company lawyer that he funneled bribes to Mexican officials, said Paul Pelletier, a former federal prosecutor.

“If somebody put the kibosh on the investigation, a good prosecutor would ask a lot of questions to figure out why,” said Pelletier of Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, who previously supervised foreign bribery cases. “It may not be just about the bribery scheme anymore. The questions about why it was or wasn’t investigated fully are going to have potential legal ramifications for the company and individuals, which is why the company would want to dig in there.”

The Justice Department is investigating potential criminal charges under the Foreign Corrupt Practices Act, according to a person familiar with the probe who wasn’t authorized to speak publicly. The FCPA bans payments by companies or their agents to foreign governments to obtain or retain business.

The probe will probably expand beyond Mexico if the company or government unearth red flags elsewhere or if the government questions both management’s response to reports of misconduct and its current compliance program, said Amy Conway-Hatcher, a former federal prosecutor at Kaye Scholer in Washington.

“The investigation alone could cost Walmart in the tens of millions of dollars or more, and that’s if it’s limited to Mexico,” Conway-Hatcher said. “The cost of a global investigation under these circumstances could rise into the hundreds of millions. This would not include penalties and fines if charges are brought.”

Government investigators, she said, “will look at the acts of individuals to see if they can prove violations of law, how high up it went, who knew about it, who authorized it, and the extent to which there was any coverup.”

In an FCPA crackdown, the government settled 57 cases against companies from 2005 through 2011, reaping $4.1 billion for the U.S. treasury.

In 2008, Siemens, Europe’s largest engineering company, agreed to pay $800 million to the U.S. and $814 million to German authorities. Siemens also spent $1 billion on lawyers and accountants and its internal controls.

Wal-Mart has hired the Jones Day law firm to investigate its Mexican operations, as well as auditing firm KPMG and law firm Greenberg Traurig for a compliance review of its global operations, said a person familiar with the matter.

The company also said it created a new position to monitor global compliance with the FCPA. The officer will be based in the retailer’s headquarters in Bentonville, Ark., the company said yesterday in a statement.

The Times reported that a former executive in Wal-Mart de Mexico’s real estate department, Sergio Cicero Zapata, emailed a former senior lawyer in September 2005 to describe how he had funneled cash bribes to government officials through fixers known as “gestores.” Top executives, the paper reported, focused more on damage control than on uncovering misconduct.