Occidental Petroleum Corp. Chief Executive Ray Irani is expected to soon set a date to step down as investor anger over his high pay mounts, according to a report in the Wall Street Journal.

People familiar with the matter said that Irani is expected at next month’s board meeting to name a date in 2011 for retiring as CEO, but is expected continue as chairman, according to a story in Wednesday’s Journal. Irani declined to comment for the story.

Irani, 75, has topped the Los Angeles Business Journal’s list of highest paid chief executives in the Los Angeles area for five years, with a $31.4 million compensation package in 2009, down 48 percent from the previous year.

Stephen Chazen, 64, who was promoted to chief operating officer last month and already held the title of president, is considered Irani’s most likely successor.

The report comes after two of Occidental’s institutional shareholders launched proxy fight for seats on the company’s board. Relational Investors LLC and the California State Teachers’ Retirement System, which together own about 1 percent of the company’s shares, said they hope to unseat at least four of Occidental’s 13 directors at next year’s annual meeting.

In addition to issues over Irani’s compensation, which in some years has exceeded $87 million, the institutions have criticized Occidental for not announcing a formal CEO-succession plan as Irani reached the company’s retirement age of 75 for directors. The board waived the retirement-age rule for Irani and two other directors at this year’s annual meeting.

Shares were up $3.40, or 4.6 percent, to $76.48 in midday trading on the New York Stock Exchange.