This story was excerpted from Maria Guardado’s Giants Beat newsletter. To read the full newsletter, click here. And subscribe to get it regularly in your inbox.

SAN FRANCISCO -- The Giants have struggled to find dependable late-inning relievers outside of closer Camilo Doval and Tyler Rogers this season, but they have another option who is getting close to joining the bullpen mix.

Veteran right-hander Luke Jackson, who signed a two-year, $11.5 million deal in January, began a rehab assignment with Single-A San Jose on Sunday, tossing a scoreless inning on nine pitches while sitting at 95 mph with his fastball.

“Really good,” said manager Gabe Kapler, who also watched Jackson pitch in an extended Spring Training game in Arizona last week. “Really efficient inning in San Jose. I’m excited. He’s getting closer. Obviously, we’re still probably a couple of weeks away, but we’re moving in the right direction.”

Jackson, 31, missed the 2022 campaign after undergoing Tommy John surgery, but he enjoyed a career-best season for the World Series champion Braves in 2021, logging a 1.98 ERA with 70 strikeouts over 63 2/3 innings.

It can take a while for pitchers to regain their form after returning from Tommy John surgery (John Brebbia, for example, recorded a 5.89 ERA in his first 18 post-surgery appearances for the Giants in 2021), but if Jackson bounces back as expected, he could provide a much-needed boost to San Francisco’s bullpen, which entered Tuesday with the third-highest ERA (5.84) in the Majors.

Jackson is currently on the 60-day injured list and will be eligible to return as soon as May 29, so it wouldn’t be a surprise if the Giants welcome him back to their relief corps sometime in early June.

“That’s a strong possibility,” Kapler said. “We’ll see how he progresses. Two weeks is a long ways away. At the same time, it’s kind of right around the corner.”