TAMPA — Jonathan Loáisiga is happy to be back with the Yankees, even if he won’t be pitching for them for likely the first two months of the season.

After undergoing UCL surgery last April, and then re-signing with the Yankees in December, Loáisiga is aiming to be back by late May or early June, the reliever said Thursday.

“But you have to allow flexibility in that time frame and keep going through it and see how you feel,” Loáisiga said through an interpreter after the second day of workouts at Steinbrenner Field. “I feel really good physically and mentally. I feel strong. It’s been a long process, but at the same time, we’re exactly where we should be as far as schedule. We want to make sure the plan to get back on the field, we follow it exactly. There’s no rush to get back on the field, but at the same time, we’re making great steps.”

Loáisiga has been one of the Yankees’ most effective relievers over the last few years, but that talent has largely been overshadowed by injuries to his shoulder and then last year his elbow.

But the 30-year-old right-hander is hoping this year can be different once he returns to the mound — and a bullpen that should be deep and a strength of the Yankees — after signing a one-year, $5 million contract with a $5 million team option for 2026.

“Coming back here, it was very important to me to come back,” Loaisiga said. “I felt that I owed it to the team and to the fans — I think I only pitched four innings last year. Deep in my heart, I felt like that’s what I wanted to do. That was important for me to come back here.”

Gerrit Cole threw live batting practice Thursday, tossing 25 pitches and coming out of it feeling healthy.

“Lot of strikes, some good shapes, too,” Cole said. “It was pretty good. Three 95s [mph] or something like that. It’s a good place.”

Minor league reliever Eric Reyzelman was discharged from the hospital Thursday morning and rejoined the Yankees after having an allergic reaction at the team’s facility Wednesday morning.

“Obviously a scary day [Wednesday],” manager Aaron Boone said. “He came in here today in good spirits, so I got to see him. I talked to him a couple times [Wednesday]. Seemed like he really started to turn the corner in a good way late in the afternoon and then was good when I touched base with him in the evening. He looked really good and hopefully out of the woods today. Discharged and came in, hung out a little bit. Obviously a scary situation, but happy to report he’s doing well.”

The Yankees unveiled the new wing of their facility at Steinbrenner Field to the media on Thursday, which includes an indoor/outdoor gym, state-of-the-art recovery spaces and an indoor/outdoor food lounge.

The project began as soon as spring training ended last year and will be a boon for the Rays to use this season when they take over Steinbrenner Field (after the roof at Tropicana Field was torn off by a hurricane in October).

“It’s unbelievable,” Cole said. “They’ve done a fantastic job. … Everything’s new, the space is great, there’s a ton of natural light, high ceilings, good privacy. … Last year, it was like, run down there, run down there and then run down there. It makes things more efficient. It feels good to have a really nice facility and new players come in, the word will get out.

“The Rays will enjoy this, I can tell you that.”