Activist hedge fund Starboard Value has built a 9.8 percent stake in small health insurer and pharmacy-benefits manager Magellan Health.

Though Starboard partners and founders Jeffrey Smith and Mark Mitchell said in a regulatory filing that they do not at the moment have an official plan for Magellan, a source familiar with the matter told CNBC that the fund could consider advocating for a potential sale or managerial changes to help boost shareholder value.

Magellan shares, which were down 35 percent this year, jumped nearly 8 percent Thursday following news of the Starboard stake.

Smith and Mitchell said in the regulatory filing that they believe "the shares, when purchased, were undervalued and represented an attractive investment opportunity." The fund reported that it owns 2.3 million shares and made purchases from Nov. 7 through Dec. 12.

The hedge fund said that it may eventually decide to open dialogue with Magellan — worth about $1.5 billion — to discuss the business, including ownership structure, board composition and potential business combinations, according to the Securities and Exchange Commission filing.

Starboard Value declined to comment for this story while Magellan Health did not respond to CNBC's request for comment.

The company has disappointed investors several times this year by cutting its 2018 earnings forecast three times. In an attempt to remedy poor performance in its insurance segment, the Scottsdale, Arizona-based company said last month that it had fired the head of its largest division, Sam Srivastava.

"In light of our recent performance and lowering of guidance, we acknowledge that our financial results have been below our expectations," Magellan CEO Barry M. Smith said in a release last month. "In the short-term, we expect the environment to remain challenging, but we see significant long-term opportunity in both our Healthcare and Pharmacy businesses."

Starboard also had a small position in medical equipment and supplies company Baxter International at the end of the third quarter with 727,000 shares.