Bridgewater Associates Chief Executive David McCormick told staff Thursday that he was considering resigning to run for U.S. Senate in Pennsylvania, and that he planned to decide within the next few weeks, said people familiar with the matter.

Mr. McCormick has been discussing with Bridgewater’s leadership a possible exit from the hedge fund, and the firm’s board is drawing up potential replacement plans, some of the people familiar with the matter said.

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Bridgewater Associates Chief Executive David McCormick told staff Thursday that he was considering resigning to run for U.S. Senate in Pennsylvania, and that he planned to decide within the next few weeks, said people familiar with the matter.

Mr. McCormick has been discussing with Bridgewater’s leadership a possible exit from the hedge fund, and the firm’s board is drawing up potential replacement plans, some of the people familiar with the matter said.

On a call Thursday, Bridgewater executives told staff they were already at work on a transition in case Mr. McCormick left. A former Treasury Department official under President George W. Bush, Mr. McCormick has been at Bridgewater, the world’s biggest hedge fund, for more than a decade and was named co-CEO in 2017. He has been sole CEO only since last year, when the other co-CEO, Eileen Murray, left in an acrimonious pay dispute.

Mr. McCormick’s interest in the Republican primary for the vacant Pennsylvania seat was earlier reported by Politico.

It wasn’t immediately clear who might succeed Mr. McCormick; Bridgewater founder Ray Dalio, who is co-chief investment officer, has publicly promised to step back from the firm’s operations. People familiar with the matter said Mr. McCormick’s deputy, Nir Bar Dea, could get a quick promotion, or that a member of Bridgewater’s board could step in on an interim or longer-term basis.

A West Point graduate and Gulf War veteran, Mr. McCormick would join a crowded Republican primary to succeed retiring GOP Sen. Pat Toomey. Celebrity surgeon Mehmet Oz filed paperwork Tuesday to run for the seat, joining Carla Sands, who served as former President Donald Trump’s ambassador to Denmark, and businessman Jeff Bartos in the GOP field.

On the staff call Thursday, Mr. Dalio also addressed controversial remarks he made this week on human-rights considerations when investing in China. “I can’t be an expert on those types of things,” he told CNBC, adding later, “should I not invest in the United States because other things—our own human rights issues or other things?”

Mr. Dalio said on the staff call Thursday he had answered the question poorly, but that the firm’s investments in China were important to consider.

—Michael C. Bender contributed to this article.

Write to Juliet Chung at juliet.chung@wsj.com and Rob Copeland at rob.copeland@wsj.com