Wednesday, the Bucs drafted Mesa's son, outfielder Juan, in the 23rd round of the First-Year Player Draft.
"I'm proud. That was my dream to see him be a ballplayer and see what he could do," Jose Mesa said.
"He's got a lot of potential. It's just a matter of him going out there and proving what he can do."
At his father's urging, Juan, 20, worked out privately with the Pirates last summer. Pittsburgh manager Lloyd McClendon was impressed with what he saw from the 6-foot-2, 190-pound left fielder.
"I thought he had a little juice in the bat," said McClendon. "He's a strong kid. It was pretty interesting. I liked the size of his body, the agility and the bat speed. I think he's got a chance."
Because the native Dominican had enrolled briefly at Miami Dade Junior College prior to the workout, the Pirates could not sign Juan Mesa to a professional contract at the time.
"As we later learned, because of going [college], he had to enter the draft," said Pirates GM Dave Littlefield.
Soon after Juan was drafted, the 39-year-old Bucs closer was asked if he thought there might be a chance that he'd one day play in the big leagues with his son. "If he makes it quick," Jose Mesa said, smiling. "I'm not going to stick around forever."
Ed Eagle is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.