Activist investor Bill Ackman has disclosed a nearly 10 percent stake in Chipotle, and said that he wants to open discussions with the US fast food chain's management.

According to a document filed Tuesday with the Securities and Exchange Commission, Ackman and his Pershing Square fund now hold 9.9 percent of Chipotle stock.

Ackman, who has a reputation for involving himself in the affairs of the companies he invests in, said in the filing that his fund intends "to engage in discussions" with Chipotle's management, board and other stockholders and interested parties.

The subject of those discussions, according to the filing, "may relate to the governance and board composition, business, operations, cost structure, management, assets, capitalization, financial condition, strategic plans, and the future of the issuer."

The chain, which specializes in Mexican-inspired food, has plunged in value in recent months because of repeated food safety issues at its restaurants.

Ackman's filing said his fund believes Chipotle is undervalued but that it "has a strong brand, differentiated offering, enormous growth opportunity, and visionary leadership," making it an attractive investment.

Chipotle shares are down around 45 percent from their peak in mid-2015. News of Ackman's investment, however, sparked a six percent jump Chipotle share prices in electronic trading after the close of trading Tuesday on Wall Street.