NEW YORK — There won’t be too many pregame pressers this season that feature more positive Yankees injury news from manager Aaron Boone than Tuesday’s media session at Yankee Stadium.

Ace Gerrit Cole continues to make progress in his throwing program, tossing a second bullpen session. Everything has gone well with the right-hander’s rehab since he was shut down in spring training with nerve inflammation in his elbow.

Veteran infielder DJ LeMahieu is slowly ramping up in baseball activities, getting closer to in-game action after the setback he suffered late last month. LeMahieu was taking grounders at third base on Tuesday afternoon, planting and moving laterally with his injured right foot.

Both of those two key pieces could travel with the Yankees on their upcoming road trip to Tampa, continuing to rehab at the organization’s complex, Boone said.

Meanwhile, reliever Nick Burdi and infielder Oswald Peraza are starting rehab assignments.

Burdi (hip inflammation) will pitch in Triple-A Scranton/Wilkes-Barre. His first rehab outing (with Double-A Somerset) was rained out on Sunday — the same storm that forced the Yankees to play eight innings in a monsoon in the Bronx — but he still tossed one live inning against some of the club’s minor-league hitters.

Peraza (shoulder strain) will suit up for the Class-A Tarpons on Tuesday, his first in-game appearance since early in Grapefruit League play this spring. Like Cole, Peraza needs to build up with a full spring training-like workload, so he’ll be on assignment for the next few weeks, at least.

It was the update that Boone delivered at the very end of his presser that had fans buzzing on social media, though.

Top prospect Jasson Domínguez is inside of two weeks from starting a rehab assignment, Boone said.

“I think he’s middle of the month to where he’ll start in games,” Boone said. “He’s getting close.”

The plan, as of now, is for Domínguez to play his first couple weeks strictly as a designated hitter. Eventually, he’ll get reps in the outfield again, using his surgically repaired elbow in games for the first time.

Domínguez won’t be rushed back. Not from an injury as serious as Tommy John surgery and not with four healthy and productive outfielders on the active roster. But Domínguez competing in games, whether it’s in the Bronx, Tampa or Scranton/Wilkes-Barre, is a big step.

Remember, Domínguez is far from a finished product. As he gets comfortable physically in the aftermath of his surgery, he’ll need to continue developing against talented pitching. He’s only logged 62 plate appearances above Double-A (31 over nine games in Triple-A and 31 in eight games with the big-league club last summer), so a rehab assignment will be more significant than only a chance to get his timing back.