Google is nearing a deal with the European Union that could resolve the antitrust investigation there, potentially lifting a significant legal cloud over the American search giant in one of its most important markets, officials said Tuesday.

The company has proposed several remedies to complaints that it has used its dominance in the Internet market to hurt competitors in search, travel and other industries. But both sides have expressed an eagerness to reach a negotiated settlement instead of engaging in a protracted legal battle of the sort that entangled Microsoft for years.

The European Union “considers Google’s proposals as a good basis for further talks and has reached a good level of understanding with Google,” said Antoine Colombani, spokesman for Joaquin Almunia, the top antitrust official in Europe. “There will soon be discussions at technical levels. We hope this process will lead to remedies addressing our concerns.”

Officials have declined to elaborate on the details of a possible settlement, but the progress makes it less likely that Google will face a formal legal procedure that could lead to a fine of up to $4 billion.

A settlement probably would require changes to Google business practices that could affect users worldwide. The U.S. Federal Trade Commission, which also is investigating Google, is following the E.U. case closely, as are regulators in other nations.

Google had no immediate comment on reports that the negotiations were going well. FairSearch, an industry coalition critical of Google, said it “would welcome a rapid, substantive and legally enforceable change to Google’s business practices that steer users to its own products and away from others. Only when these practices end will Google’s ongoing harm to consumers and innovators end.”