Sean Penn tried to be super stealthy when he interviewed El Chapo, but he was a loud bragger in the middle of a restaurant just before the story broke ... according to Page Six.

Sean was reportedly holding court during Golden Globes weekend at the famed Polo Lounge, a watering hole for celebs. Page Six says Penn was strategizing with his crew which included a former State Dept. employee. One spy said, "He was running around like Woodward and Bernstein at the Washington Post ... they were loudly talking about El Chapo."

The spy says Penn and company were concerned that Mexican actress Kate del Castillo "was going to write her side of the story ... [Penn] was like, 'She wants to be on Charlie Rose instead of me!'"

Page Six got a "no comment" from Penn's rep.