Chipotle Mexican Grill and Bill Ackman are nearing a settlement that would give the hedge fund billionaire a say in the burrito chain's boardroom, according to The Wall Street Journal.

A source told CNBC that talks are ongoing between the two parties, but are fluid and may not result in an agreement. This person said it is unclear what the parameters of an Ackman-Chipotle settlement would be.



Earlier this month, Ackman said he has had an "extremely constructive relationship" with the company since he took a nearly 10 percent stake in September.



A settlement could smooth tensions between Chipotle and its shareholders, who have been frustrated by the company's attempts to recover from cratering sales in the wake of a foodborne illness outbreak.

The Denver-based company has faced criticism from investors for having an insular board that lacked racial and gender diversity, which, according to CtW Investment Group. Critics also say the board doesn't have enough experience in the restaurant industry.

"The food-safety crisis really exposed shortcomings in Chipotle's management and governance," Jeff Gramm, a small activist who owns about $8 million in shares, told the Wall Street Journal.



In April, CtW addressed Chipotle shareholders in a letter asking them to withhold support for the reelection of two directors during annual shareholders' meeting in May. While the directors remained part of the board, at least for another year, Chipotle hoped to gain back investor's trust by interviewing new members in August.

So far, the company has yet to make any announcements about new hires.

"The dialogue we've had so far with Pershing has talked about driving long-term shareholder value, talks about recovering the business model and from what they've said so far, they believe Chipotle is a special brand and we're going through a tough time right now and they want, just like everyone else, to see us recover our sales, recover our business and if we do that we're going to get back to our previous stock price and add shareholder value from there," Jack Hartung, Chipotle's CFO said on CNBC's "Mad Money" on last week.



Read the full report from The Wall Street Journal.