Activist investor Engaged Capital is planning a proxy fight for three board seats at high-end burger chain Shake Shack, the Wall Street Journal reported on Sunday, citing people familiar with the matter.

Including swaps, Engaged has a roughly 6.6% stake in the restaurant chain, the report added.

Engaged has determined ways to double the company's profitability within two years and believes the burger chain should get rid of its staggered board, which means that not all directors are up for election at the same time, according to the report.

Engaged has been in talks with the company's management for over six months and sent a letter to the company’s board in March detailing its proposal for new directors and other changes to help boost the restaurant chain’s lagging stock price without an agreement, the people told WSJ.

Engaged Capital and Shake Shack did not immediately respond to a request for comment.

(Reporting by Urvi Dugar in Bengaluru; Editing by Lisa Shumaker)