Yankees pitcher Gerrit Cole looks on from the dugout during...

Yankees pitcher Gerrit Cole looks on from the dugout during an MLB baseball game against the Minnesota Twins at Yankee Stadium on Thursday, June 6, 2024. Credit: Kathleen Malone-Van Dyke

BOSTON — Will Gerrit Cole’s next appearance on a mound be in the big leagues?

That determination had not been made as of Saturday, but, as Cole told reporters Friday night in Rochester after his third rehab start, “We’ve got to make that decision in the next 24, 48 hours.”

He struck out 10 and allowed two hits and an unearned run in 4 1⁄3 innings with Triple-A Scranton/Wilkes-Barre on Friday. Less than a day later, what could only be described as a jovial Cole arrived in Fenway Park’s visitor’s clubhouse.

The righthander said discussions about the when and where of his next outing had yet to begin in earnest but will soon.

“I’m obviously feeling good today,” Cole said Saturday. “And I felt really good last night. I want to look at the computer, too. It usually takes a day to process all the numbers and stuff. The gamesmanship was good last night. We were picking good pitches and moving the ball around and meeting the demands of the game. Then we’ll get some objective feedback from the computer and see exactly where the pitches were located and the velocity and whatnot. My eyes said it was pretty good, so I’m assuming it’s going to be pretty good, but you’ve just got to be thorough in that situation.”

Though the decision won’t be solely Cole’s, the reality is that the reigning American League Cy Young Award winner is going to have the final say on where he starts next.

If Cole — who has a 0.73 ERA and a 0.49 WHIP with 19 strikeouts in 12 1⁄3 innings in his three rehab starts — pushes hard to come back next week against the Orioles, it’s difficult to imagine the Yankees telling him no.

Conversely, if Cole thinks he needs at least one more start in the minors, the chance is zero that the club would insist he come to the big leagues.

“Obviously, he’s going to have a huge say in that and especially if it’s another rehab start,” Aaron Boone said. “But at the same time, there’s also a lot of good and smart people involved. I think we’ve all done a really nice job so far in his buildup and getting him ready. So we’ll have those conversations honestly and openly and Gerrit [will be] right involved in that.”

Cole, who threw 70 pitches Friday night in the continuation of what has been a slow but steady buildup, saw his fastball sit in the range of 95 to 96 mph and peak just under 98.

“I’m very much wanting to get back very soon,” Cole said Friday. “What a fun club they are right now. That’s part of the reason why I’m trying to make sure I’m in a good spot to help them.”

Cole, who said he felt “really strong” at the end of Friday’s outing, indicated afterward that he doesn’t want to put the Yankees’ bullpen in a bind by coming back too soon.

“I’ve just got to get the pitch count up,” he said. “I mean, the team’s playing well. It’s not a situation where you come in and, like, disrupt the distribution of innings with your bullpen when everything’s flowing so well. And making sure that you’re laying some rubber on the road a little bit so if you do get into a spot [in-game jam], you have enough to get out of it.’’

Whenever Cole returns, he will be joining a rotation that has thrived in his absence.

Going into Carlos Rodon’s start against the Red Sox on Saturday night, the Yankees had the lowest starters’ ERA in the majors at 2.77 (the Phillies were next at 2.82).

The group had allowed three or fewer earned runs in 61 of 72 starts, two or fewer earned runs in 50 starts and one or fewer earned runs in 36 starts. The group collectively has allowed more than four earned runs only three times, the fewest in the majors.

Entering Saturday, the club’s starters had thrown at least four innings in each of their 72 starts, the longest single-season streak in franchise history and tied with the 2004 A’s for the eighth-longest season-opening streak by any big-league club since 1900.

Luis Gil is 9-1 with a 2.03 ERA and a 0.98 WHIP. Rodon was 9-2, 2.93, 1.05 entering Saturday. Marcus Stroman is 6-2, 2.82, 1.24; Clarke Schmidt is 5-3, 2.52, 1.14, and Cody Poteet — who has filled in for the injured Schmidt — is 3-0, 2.14, 1.05. Nestor Cortes is 3-5 but has a very respectable 3.59 ERA and 1.12 WHIP.

For those reasons, Cole produced a wry smile when asked Friday about the rotation “weathering the storm” with him out.

“I feel like weathering the storm is a bit of an understatement,” he said. “I feel like they’ve excelled. One of the top rotations in the league so far. The depth has been great, obviously. Cody comes in and doesn’t miss a beat. So a lot of respect to those guys.

“You can talk to guys on the side and be supportive, but it’s another thing to get between the lines and put it up. So super-proud of what they’ve been doing, and I know they are too.”

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