SCOTTSDALE, Ariz. — Brian Cashman hasn’t wasted much time this offseason. Even before arriving here for the annual general managers’ meetings, Cashman, who has put bullpen improvement near the top of his priority list, touched base with the agent for Aroldis Chapman, expected to be the most sought-after free-agent reliever.

“I’ve started making my phone calls of free agents,” the Yankees’ GM said early Monday afternoon. “I’ve reached out to a number of them.”

The Yankees acquired Chapman last offseason in a trade with the Reds and dealt him to the Cubs before the Aug. 1 trade deadline for a package that included highly regarded prospect Gleyber Torres. The lefty with the 104-mph fastball is the headliner among the free-agent class of relievers, which includes Kenley Jansen of the Dodgers and Mark Melancon of the Nationals. (Melancon came up with the Yankees, who drafted him in the ninth round in 2009.)

Chapman, 28, who showed signs of fatigue in the postseason, shined throughout the season. He posted a 2.01 ERA in 31 appearances with the Yankees, recording 20 saves, before saving 16 for the Cubs and posting a 1.01 ERA in 28 appearances.

It is no secret that Chapman enjoyed pitching for the Yankees and would be interested — at the right price — in a reunion.

Cashman said his interest in bolstering his bullpen is not a reflection on Dellin Betances, who became the closer after Chapman and then Andrew Miller were traded. Betances had 12 saves in 17 chances.

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“I just think he was tired,” Cashman said of Betances, who was used more than any other reliever in baseball the last three years — 70 appearances in 2014, 74 in 2015 and 73 this past season.

Betances allowed at least one run in six of his last nine appearances, which raised his ERA from 2.05 to 3.08.

“As you saw in the postseason, too, when guys get used a lot, they can start to wear down,” Cashman said, a reference to Miller and Chapman, who both seemed to tire during the World Series.

Still, he left plenty to read between the lines.

“I just want to bring in more talent, so it’s too early to say who’s going to do what,” said Cashman, who has been given “a number” he wouldn’t specify from managing general partner Hal Steinbrenner on what he can spend this offseason. “It depends how the winter goes. So right now, yeah, he’d [Betances] be the closer if the season was starting today, but it’s not.”

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Perhaps more important, Cashman wants to add to a rotation that has, he said, three pitchers “locked” into their spots — Masahiro Tanaka, Michael Pineda and CC Sabathia.

“Then you’ve got a whole bunch of young guys that are going to compete,” Cashman said, mentioning Adam Warren, Bryan Mitchell, Luis Cessa, Chad Green and Luis Severino.

There’s a reason Cashman wants to add “certainty” to the mix, because there isn’t much. Tanaka was one of the best in the American League last season — he went 14-4 with a 3.07 ERA — but there’s nothing but questions after him. Pineda (6-12, 4.82) was wildly inconsistent, and although Sabathia had a strong second half to finish 9-12 with a 3.91 ERA, the lefthander will turn 37 in July.

“We certainly would like to add to it or certainly would like to be in a position to feel that you can put some more certainty in there or more competition in there,” Cashman said. “It’s probably a thin starting pitching market. There’s a number of different relievers in the market. Certainly more relievers in this free agency than there are starters of quality. And the trade route’s obviously an area we’ll see what develops over time.”