SAN DIEGO — Carlos Beltran doesn’t possess David Ortiz’s larger-than-life Big Papi persona or the cartoonish charm of the ageless Bartolo Colon.

But as the third-oldest player to be selected for Tuesday night’s All-Star Game, his ninth overall, Beltran is a valuable commodity: a coveted hitter who might be on the trade market before too long.

That was the gist of the questions directed at Beltran, 39, during Monday’s media availability, when he alternately talked about the Yankees’ iffy playoff chances and his own potential departure from the Bronx.

Twice before, Beltran has been used as midseason trade bait, by the Royals in 2004 and the Mets in 2011.

The Royals, via a three-way deal involving the A’s that sent Beltran to the Astros, received Mark Teahen, Mike Wood and John Buck in the 2-04 trade. The Mets acquired Zack Wheeler from the Giants in the 2011 swap.

As for whether the Yankees will consider him a chip in a possible rebuild, Beltran shrugged.

“I’m not going to push it,” he said. “I love where I am. At the same time, the organization will make the decisions that are important to them.”

With a slash line of .299/.338/.550, 19 home runs and 56 RBIs in 83 games, the switch-hitting Beltran would be a potent addition to any contender’s lineup. Based on his recent knee issues and lack of range in the field, however, he probably is best suited for DH duty, a liability that could restrict the Yankees’ options. Beltran — who has roughly $7 million left on his three-year, $45-million deal — also has 15 teams on his limited no-trade list.

“This is a business,” he said. “We’re employees, man.”

That’s not to say Beltran is ready to jump ship in the Bronx. He wants to stay put for a run at the postseason and still has faith that the Yankees can build off their series win over the AL Central-leading Indians before the break.

With a Hall of Fame plaque close to being clinched, Beltran doesn’t have many goals remaining, other than winning a World Series, the one thing that has eluded him in his 19-year career. But the Yankees will have to step up their play to get him deep into October this season.

“I do feel like we can be competitors,” Beltran said. “But it’s got to happen now in the second half. We have to find a way to play better baseball.”

Then again, this year probably won’t be the end of Beltran’s pursuit of a ring. Similar to Ortiz, who is on pace for 40 home runs at age 40, Beltran isn’t feeling all that old lately.

“Age, for me, doesn’t mean anything,” he said. “What’s important for me is passion, and my passion for the game is above everything.”