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Chicago White Sox manager Tony La Russa’s phone rang before a session with reporters Saturday morning at Camelback Ranch.

“We signed who?” La Russa joked as he glanced at the phone.

A few hours later, the Sox did add to their bullpen, reportedly signing reliever Joe Kelly to a two-year deal, according to USA Today’s Bob Nightengale.

The Sox also signed veteran second baseman Josh Harrison, pending a physical, according to a tweet from MSM Sports agency. It’s a one-year, $5.5 million deal, including a $1.5 million buyout on the club option for 2023, according to The Athletic.

Kelly, 33, is 50-29 with a 3.83 ERA and 619 strikeouts in 365 games (80 starts) during a 10-year career with the St. Louis Cardinals (2012-14), Boston Red Sox (2014-18) and Los Angeles Dodgers (2019-21). The right-hander had a 2.86 ERA in 48 relief appearances for the Dodgers last season with 50 strikeouts and 15 walks in 44 innings.

Pitching depth is always important. And with the shortened spring training because of the lockout, it’s a top priority for the Sox.

La Russa reiterated that point earlier Saturday before the news of Kelly’s signing.

“All 30 (teams) are going to say that depth is going to be critical,” La Russa said. “Innings are going to be precious. If you got five starters and three of them get you to the second part of the game so you’re not running the bullpen out there every day, it’s going to be the story of at least the first couple months (of the regular season). To (have) really good stamina.

“Every organization’s depth is going to be tapped. Especially if you take the attitude of health first.”

Kelly joins Kendall Graveman as new members of the bullpen. Graveman and the Sox agreed to a three-year, $24 million contract before the lockout.

Dodgers reliever Joe Kelly delivers against the Braves during the National League Championship Series on Oct. 17, 2021, in Atlanta.
Dodgers reliever Joe Kelly delivers against the Braves during the National League Championship Series on Oct. 17, 2021, in Atlanta.

Sox closer Liam Hendriks expressed excitement about watching Graveman when he met with reporters hours before Kelly’s reported deal.

“He has the stuff to be good out there,” Hendriks said of Graveman on Saturday morning. “It’s going to be fun to watch and fun to be a part of watching his progression in the bullpen.”

Kelly provides another boost to a pen. The Sox are still contemplating what’s ahead for Craig Kimbrel, whose name has come up in trade rumors. Asked Saturday, La Russa said he anticipates Kimbrel will be on the opening-day roster.

“I was really encouraged that when (executive vice president) Kenny (Williams) and (general manager) Rick (Hahn) first talked to Craig and his agent, he really likes it here. But he really likes closing. And I like the first part of it a lot because I had him in Boston (in 2018). He’s a first-class person, family guy. He fit in very well with our team. He’s got a chance to be a Hall of Fame closer.

“Rock and a hard place. But I know him. Whatever role he has, he’s too competitive, going to give it his best. If he’s here, another dynamite arm. We’ll see.”

The Harrison signing would address a need at second base.

The two-time All-Star has a career .274/.318/.401 slash line with 64 home runs and 351 RBIs in 1,049 games with the Pittsburgh Pirates (2011-18), Detroit Tigers (2019), Washington Nationals (2020-21) and Oakland Athletics (2021). He was an All-Star in 2014 and ’17.

Harrison, 34, had a combined .279/.341/.400 slash line in 138 games last season with the Nationals (90 games) and A’s (48). He played 102 games at second base in 2021 but also made starts at third, shortstop and all three outfield spots.

The Athletics' Josh Harrison slides into third base during a game against the Astros on Sept. 24, 2021, in Oakland, Calif.
The Athletics’ Josh Harrison slides into third base during a game against the Astros on Sept. 24, 2021, in Oakland, Calif.

During the offseason, the Sox declined second baseman César Hernández’s club option. He later signed with the Washington Nationals. The Sox did bring back infielder/outfielder Leury García on a three-year, $16.5 million deal before the lockout. García’s versatility is one of his strengths.

Second base and the bullpen were among the areas worth watching for possible post-lockout additions. Asked earlier Saturday if pitching depth was the biggest need, La Russa said “absolutely.”

“Pitching and defense is going to be the key to our team,” La Russa said. “We’ve got a deep enough offense to score runs. Especially if we improve. Pitching and defensive side, the depth side, with the short spring training and 162 (games) and so many days. When in doubt, you add some pitching help.”