BRUSSELS, Jan 24 (Reuters) - U.S. online retailer Amazon AMZN.O has offered to drop some clauses from its e-book deals with publishers in a bid to end an EU antitrust investigation and stave off a possible fine, a person familiar with the matter said on Tuesday.

The proposal means that Amazon, the biggest e-book distributor in Europe, will not force publishers to give them terms as good as those for rivals, the source said.

The European Commission is expected to seek feedback from rivals and customers before deciding whether to accept the proposal or demand more, the person said.

The EU competition enforcer, which launched an investigation into the company in June 2015 on concerns that the disputed terms may make it difficult for other e-book publishers to compete, did not respond to an email seeking immediate comment.

The investigation focuses on Amazon's e-books in English and German. Under EU antitrust rules, companies can be fined up to 10 percent of their global turnover for violating laws.

The Commission is also probing Amazon over its tax deal with Luxembourg, part of a crackdown on such deals in the 28-country bloc.

(Reporting by Foo Yun Chee; editing by Jason Neely) ((foo.yunchee@thomsonreuters.com)(+32 2 287 6844)(Reuters Messaging: foo.yunchee.thomsonreuters.com@reuters.net))