PHOENIX -- Johnny Cueto sat in the visiting dugout at Chase Field on Saturday, picked up a baseball and demonstrated the differences between the grips for a slider and a sinker.

Then, the veteran right-hander shared an anecdote from his time rehabbing from Tommy John surgery at the Giants' facilities in Scottsdale, Ariz., over the past few months.

“He was throwing the slider holding it like a sinker,” Cueto said with a laugh, via an interpreter, about one of the young pitchers at the Giants’ complex. “I said, ‘How do you throw a slider like that?’”

That's the benefit of having Cueto at a place where many of the Giants' Rookie-level pitchers and international signings begin their professional careers. But Cueto isn’t just passing along knowledge. He’s working his way back from the elbow reconstruction surgery he had last August.

For the second time during his throwing program, Cueto threw a bullpen session at Chase Field, where the Giants are playing a three-game series this weekend. A month ago, the right-hander threw off the mound in the visiting bullpen, and he was there again several hours before Saturday’s game.

Cueto is throwing 40-pitch bullpen sessions every Tuesday and Saturday, and this past Tuesday, he began mixing in his full arsenal of pitches after previously only throwing fastballs. He could progress to throwing batting practice in July, and he remains optimistic that he’ll pitch in the big leagues later this season.

“I hope that’s possible,” Cueto said. “I feel really good, and obviously if I’m able to pitch in September, I’d be really happy to be back with the team.”

Much like the last time Cueto threw a bullpen session in front of his Giants teammates and coaches on May 18, manager Bruce Bochy came away impressed.

“I’ll tell you, he’s close,” Bochy said. “He was sitting 87-88 [mph], and that’s in a bullpen session, so usually your adrenaline’s not going that high where you’re going to get that kind of velocity. So, he’s on his way. I can’t say when he will pitch, but it’s good to see him this far along.”

And as for a September return?

“I’d be surprised if he didn’t,” Bochy said.

In the meantime, Cueto will continue his throwing program while also imparting wisdom to young pitchers. The veteran said he recently taught several hurlers how he throws his changeup, a group that included Rodolfo Martinez, a 25-year-old right-hander who has pitched at Double-A but is currently rehabbing in the Arizona Rookie League.

Cueto’s primary focus may be extending his career, but he feels it’s important to also help develop the careers of others.

“Even here at the highest level, I try to work with the guys, try to teach them,” Cueto said. “That’s just my personality. I just want to share and give.”