(Reuters) - Visa shares fell 3% on Tuesday after a report said the U.S. Department of Justice plans to file a lawsuit against the world's largest payment processor, alleging it illegally monopolized the country's debit-card market.

The antitrust division of the regulator is set to file a lawsuit as soon as Tuesday, accusing Visa of a range of anti-competitive conduct, Bloomberg News reported on Monday, citing people familiar with the matter.

"We believe this is an immediate negative to shares but we caution these types of antitrust cases are notoriously known for long/winding paths in the U.S.," boutique equity research firm Monness, Crespi, Hardt & Co said.

Visa did not immediately respond to a Reuters request for comment.

FRESH ANTITRUST SCRUTINY

The company has been facing heightened scrutiny from regulators and lawmakers for years, battling allegations of a duopoly with Mastercard ( MA ). Both companies say they operate in a highly competitive environment.

"The concern appears to be that Visa is using volume-based discounts to discourage merchants from diverting debit volume to other networks," brokerage TD Cowen said.

"It appears to us that Justice needs to argue that Visa providing discounts creates a barrier to entry for new rivals that could have driven down pricing even more."

News of the potential lawsuit comes months after another major legal setback for the duo, when a judge rejected a $30 billion antitrust settlement under which Visa and Mastercard ( MA ) had agreed to limit the fees they charge merchants that accept their credit and debit cards.

Brokerage KBW estimated that the U.S. debit business likely represents 10% of Visa revenues at the high end. It said the potential lawsuit is unlikely to be material in the long-term but expects a prolonged road to resolution.

The prudent course of action for Visa would be to wait until the November election to "see the intentions of the next administration," said Odysseas Papadimitriou, CEO of personal finance firm WalletHub.

"If the next administration's intentions are anything similar to the current one, the goal should be to settle instead of fighting a legal battle. There is a lot of uncertainty when you have protracted court battles, especially against the government."

Mastercard ( MA ) shares fell 1% in morning trade. Both stocks have underperformed broader markets this year, gaining 11% and 16.5% respectively, compared with the S&P 500's near 20% gain.

(Reporting by Manya Saini and Niket Nishant in Bengaluru; Editing by Devika Syamnath)