NEW YORK -- Regardless of how active the Rays are in the market ahead of the July 31 Trade Deadline, their biggest acquisition could be getting a healthy Tyler Glasnow back in the rotation.

Glasnow, who has been sidelined since May 10 with a right forearm strain, completed his first bullpen session Tuesday since sustaining the injury, and everything checked out well. In fact, it went even better than the right-hander expected. Glasnow threw 15 pitches, all fastballs.

“My biggest focus since I’ve been on the IL is working on my lower half and staying more consistent and stronger so I can stay more directly behind the ball,” Glasnow said. “Today, surprisingly, for the first bullpen, everything felt really, really sharp, in terms of spin efficiency and stuff.”

Rays manager Kevin Cash said Glasnow is still “a ways away” from returning to the team -- and it’s important to note that the right-hander isn’t eligible to come off the 60-day injured list until July 10 -- but seeing Glasnow get back on the mound was another step in the right direction for his recovery.

“Very encouraged by his progress,” Cash said. “He’s got a ways to go, but you’ll take any positive from his effort and his workload and what’s being thrown at him so far. He’s throwing the ball with no issue, and we’ll just go through this step-by-step process of building him back up.”

Before his injury, Glasnow was enjoying one of the best first halves, if not the best, of any pitcher in the American League. In eight starts, Glasnow posted a 6-1 record and had an AL-leading 1.86 ERA. Now, the biggest thing for Glasnow will be regaining his confidence on the mound. His next step will be throwing a second bullpen session on Friday.

“That’s the biggest thing, just the confidence with each step of throwing,” Glasnow said. “But each stage, each progression, has been good. There hasn’t been a lot of soreness, so I haven’t really even thought about it.”

The benefit of having Glasnow make the trip with the team was to have pitching coach Kyle Snyder by his side as Glasnow completed his first bullpen session. Snyder has watched every step of Glasnow’s progression since he began to throw again.

“I have a lot of trust in Kyle and everyone in here and all the coaches,” Glasnow said. “It’s been cool that every time I’ve thrown, Kyle has been out there. He was out there for the bullpen, and he’s been able to see every step of the way, which is cool.”

What did Snyder think of Glasnow’s first bullpen session?

“Just a good job, [and] that it looks really good,” Glasnow said. “He was pleased, and so was I.”

Diaz out of lineup

Yandy Díaz, who has been battling a right hamstring injury over the last couple of days, was not in the Rays’ starting lineup against the Yankees on Tuesday for a second consecutive day. The injury has been nagging Diaz over the past couple of weeks, but the Rays’ third baseman has still managed to hit .361/.426/.508 with two home runs in June.

There’s some concern with Diaz’s hamstring, but he’s considered day to day.

“We’re trying to take it as a day-to-day thing,” Cash said. “I think he would be available off the bench, but we’re going to continue to monitor him. The last thing you want to do is put him out there when he’s not feeling right, and something maybe a little more severe possibly could happen.

“He’s such a big part of the offense lately; even on the homestand, he was really swinging the bat well. We don’t want to lose him for an extended period of time.”

Duffy update

Matt Duffy (left hamstring strain) will begin his process of trying to join the active roster for the first time. Duffy will take batting practice on Tuesday with the Gulf Coast League Rays and is scheduled to have four or five at-bats in a simulated game in Port Charlotte, Fla.

“He said during the homestand that he’s feeling really good, probably the best he’s felt, [and] he has not felt anything in his hamstring, which is a great sign,” Cash said. “We’ll start this back up, the build-up, the playing time. He’s still got a ways to go. Everything’s been interrupted so far. Hopefully we can get it to go with no interruptions.”

Roster move

Before Tuesday’s game, the Rays selected the contract of right-hander Andrew Kittredge and optioned Jake Faria to Triple-A Durham. Kittredge spent time with the Rays last season, but he has shown improvement down in Durham this year, going 2-1 with a 1.93 ERA in 27 appearances. He has a 0.34 ERA and 42 strikeouts over 26 1/3 innings in his last 20 appearances. Kittredge also welcomed his first child, Brooks Phillip, last week.