Starboard Value is "certainly interested in the story at Bristol-Myers," Jeffrey Smith, co-founder and CEO of the activist hedge fund, told CNBC on Tuesday.

However, Smith refused to comment on a weekend Bloomberg report about Starboard taking a stake in the embattled pharmaceutical giant, which last month agreed to buy troubled cancer drug company Celgene in a cash-and-stock deal valued at $74 billion.

Shares of Bristol-Myers Squibb closed up nearly 2 percent Monday after seesawing on the uncertainty surrounding whether Starboard took a position or not. The stock was lower Tuesday.

Deflecting repeated questions by CNBC's David Faber, Smith said in a "Squawk on the Street" interview from the New York Stock Exchange, "I am not going to discuss Bristol-Myers." But he did say, "We are certainly interested in the story at Bristol-Myers."

A request for comment from Bristol-Myers was not immediately returned.

Broadly speaking, Smith described what he considers Starboard's mission of representing the best interests of shareholders, and how disgruntled shareholders often bring insight to the hedge fund about certain situations.

"We evaluate those situations to determine whether we can have a positive impact," he explained. "Bristol-Myers might fit that profile," he said. "It might not fit that profile. We haven't made that decision."

"If we make that decision I'll tell you what, I will come on and talk to you about it," Smith added, jokingly referring to the main topic of the interview, which was Starboard's new $200 million investment in struggling pizza chain Papa John's. "I think we're here to talk about pizza," he concluded.

Starboard currently manages more than $5 billion in assets.