Bridgewater Associates was close to bringing on Joseph Jimenez, the former chief executive of Novartis AG, but may back off in the wake of public revelations about his role in payments to President Donald Trump’s personal attorney, people familiar with the matter said.

Mr. Jimenez has been thrust into the international spotlight in recent weeks for directing $1.2 million to Mr. Trump’s attorney, Michael Cohen, who is under federal investigation. Mr. Jimenez was cosignatory to a deal to pay Mr. Cohen for advice on health-care...