BRUSSELS, Oct 9 (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.

Almunia, 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.

A fifth publisher, Pearson's Penguin, was also charged in the investigation, but is not participating in the settlement with the commission, which began its inquiry last December.

"For a period of two years, the four publishers will not restrict, limit or impede e-book retailers' ability to set, alter or reduce retail prices for e-books and/or to offer discounts or promotions," the European Commission said in its Official Journal, detailing the offer under consideration.

HarperCollins, Simon & Schuster and Hachette reached a settlement with the U.S. government in April with similar proposals.

According to analysts at UBS, e-books account for about 30 percent of the U.S. book market and 20 percent of sales in Britain, but are still negligible elsewhere.