PHOENIX — The Giants, going through a bear of a season, are eager for any development that can excite them. The 15 or so players, coaches and trainers who watched Johnny Cueto throw a 40-pitch bullpen session at Chase Field on Saturday got exactly that.

“He’s further along than we thought he’d be,” manager Bruce Bochy said. “He threw really well. I think he surprised a lot of people with where he’s at, as far as his stuff, how hard he threw and his command. He’s also gotten himself in the best shape we’ve seen him in, to be honest. He’s working hard to get back.”

Cueto aired it out in two 20-pitch “innings” in his fifth bullpen session, throwing all fastballs, 9½ months after he underwent Tommy John elbow-reconstruction surgery. He is rehabbing at the Giants’ facility in nearby Scottsdale, where he threw his first four ’pens.

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In spring training, the club and Cueto expressed hope he could throw a few innings before the season ends to whet his appetite for 2020. He might get more than that.

“From what you saw today, you’ve got to believe he’s going to be pitching before the season is over,” Bochy said. “But we’re not going to rush him back. From what we saw today, we would not be surprised if he’s back this year, but it doesn’t mean he will be back.

“We’re going to do what’s right for Johnny.”

The Giants have reasons to be cautious. Setbacks often occur in Tommy John rehab and the thinking on recovery time has changed from one year to as long as 18 months. The team can’t set any timetables but has to react to how Cueto’s arm feels.

And right now?

“My arm is telling me it wants to pitch,” Cueto said through interpreter Erwin Higueros. “Right now, I feel like I’m 25 years old.”

Cueto, 33, said he has lost 21 pounds, from 245 to 224, and replaced fat with muscle. He hopes to pitch at 230.

He said he is a little surprised to be as far along as he is. While he hopes to pitch this season, he said it is not imperative because it’s more important that he be completely ready next spring.

After the season, Cueto will have two years remaining on his six-year, $130 million contract. He pitched exceptionally in his first year, helping the Giants reach the 2016 postseason, but his numbers dived considerably in 2017 as his elbow began to ache more.

He managed to post a creditable 3.23 ERA in eight starts last season despite pitching in what he described as agonizing pain.

Henry Schulman is a San Francisco Chronicle staff writer.