BRUSSELS (Reuters) - Apple Inc's antitrust case with the European Union over e-book publishing could be settled in a couple of months, European Competition Commissioner Joaquin Almunia said on Tuesday.

The EU's antitrust chief said he hoped to resolve soon an investigation into Apple and four publishers over deals setting e-book prices.

"Hopefully in the coming couple of months, we will reach a settlement," Almunia told a British Chamber of Commerce conference.

The European Commission is now market-testing an offer by Apple and the publishers in a bid to end the EU probe. The four are CBS Corp's Simon & Schuster, News Corp unit HarperCollins, French group Lagardere SCA's Hachette Livre and Verlagsgruppe Georg von Holtzbrinck, which owns Macmillan in Germany.

(Reporting by Foo Yun Chee, Writing by Ethan Bilby; Editing by Gerald E. McCormick)