PARIS — Is online gambling coming in from the cold?

When the U.S. Congress cracked down on Internet betting in 2006, the big, publicly traded European companies that had dominated the business closed up shop in the United States. Growth in the booming industry shifted away from these companies, once the darlings of the stock market, to private operators in offshore locations like Antigua and the Isle of Man.

But now, executives of some of the European companies whisper excitedly that they may soon get a second chance in the United States. Meanwhile, a number of European countries that have long maintained barriers are moving, under pressure from regulators, to legalize, and tax, online gambling.

“There’s still a lot of gambling going on, where there’s no revenue coming in to the governments,” said Gavin Kelleher, an analyst at the research firm H2 Gambling Capital in Ireland. “They realize they could use the revenue.”

The biggest potential change would be in the United States, where, perhaps within days, Representative Barney Frank, Democrat of Massachusetts, is expected to introduce legislation aimed at overturning the Unlawful Internet Gambling Enforcement Act.