They’re not ready to put names on the uniforms yet, but the Twins’ new front office leaders have identified one quality they would like to add to the worst-in-the-AL bullpen next season: Experience.

The Twins opened the 2016 season with only four relief pitchers who had more than 120 career innings as a major-league reliever, and none of the four — Glen Perkins, Kevin Jepsen, Casey Fien and Fernando Abad — remained by season’s end. That meant the Twins were relying mostly on young, inexperienced pitchers, a situation that Derek Falvey, the Twins’ new chief baseball officer, and Thad Levine, their new general manager, plan to change.

“It seemed as if the Twins had tremendous arms in the bullpen, but not a lot of experience. A lot of young guys coming out of the bullpen into extremely stressful situations,” Levine said during a “town hall” conducted at Target Field by Fox Sports North on Wednesday night. “We’ve got a lot of plus arms out there, but if you have veterans for the eighth inning, ninth inning, they can shoulder the load and take the stress off the kids.”

Levine noted that Perkins missed all but the first week of the 2016 season because of a shoulder injury that required surgery, and suggested that the Twins’ relief-corps results — a 4.63 bullpen ERA, worst in the American League — may have been different with “one of the best closers in the American League.” The Twins are shopping, he suggested, for ways to add veterans to the ’pen, and the starting rotation, too.

“The best teams have leaders in the bullpen and rotation,” Levine said, addressing a question that came just after FSN’s hourlong telecast ended. “We’d like to add a little bit more of a veteran presence.”

Perkins and Phil Hughes might be available to do just that, Falvey said during the FSN show. Both pitchers required season-ending surgery in June, but both are making progress as they prepare for a return in 2017. The Twins “are carefully monitoring their progress,” Falvey said, and Hughes, who underwent surgery to remove a rib to relieve thoracic outlet syndrome, which was restricting the blood flow in his shoulder, appears further along than Perkins.

They’ll also see more of Jose Berrios, whose first season was a disappointment: 3-7 with an 8.02 ERA in 14 starts. Twins manager Paul Molitor said he’s not discouraged by the 22-year-old righthander’s debut, even if fans were.

“I don’t like when guys get labeled as prospects before they get here,” Molitor said. “They have all these expectations, and it’s almost impossible to meet them.”

Levine said he’s confident the Twins have a future ace in their organization right now — they just don’t know who.

“Somebody in our farm system will overachieve and get to that level, will develop the way that Corey Kluber or Cliff Lee did,” Levine said.