MINNEAPOLIS -- Josh Donaldson says that his intent was not to single out Yankees ace Gerrit Cole as a lead figure in any way as part of his recent comments regarding increased enforcement of pitchers' use of sticky substances to improve their spin rates.

But it just so happened that Cole was the Yankees' starter against Donaldson and the Twins on Wednesday night at Target Field, days after Donaldson first addressed reporters in Kansas City during an extended session about his desire to see MLB crack down on pitchers' use of such foreign substances, going so far as to mention Cole by name.

"I was not bringing Gerrit Cole's name to the forefront because I'm putting him as the leader in all of this," Donaldson said. "I saw that, and now there's been [other] guys [I’ve noticed]. [Trevor] Bauer's had to answer questions about it, too. You look at the spin rate drops with him and other guys, and I think you're going to see what's happened."

Cole had a noncommittal answer when asked by New York media on Tuesday whether he had used Spider Tack, a particularly sticky substance that has come under scrutiny in baseball, to aid his pitching.

"I don’t quite know how to answer that, to be honest," Cole said. "I mean, there are customs and practices that have been passed down from older players to younger players, from the last generation of players to this generation of players. I think there are some things that are certainly out of bounds in that regard, and I’ve stood pretty firm in terms of that."

Donaldson indicated that he was prepared for possible retaliation from Cole, whose spin rate dropped on his four primary pitches -- four-seam fastball, curveball, changeup and slider -- in his June 3 start against Tampa Bay.

"I'm not in his brain," Donaldson said. "If he decides to do whatever he wants to do, do it."

"I’m not worried about it, going into the game, in any way," Twins manager Rocco Baldelli said. "I anticipate Gerrit Cole going out there and being the Gerrit Cole we’ve seen for a long time."

Donaldson, who ended up going 0-for-3 against Cole with two strikeouts on Wednesday night, said he felt it was important to speak publicly on behalf of hitters around the league in the aftermath of the discussion first rising into the public consciousness during a press conference from St. Louis manager Mike Shildt, who saw pitcher Giovanny Gallegos have a hat confiscated by umpire Joe West during a May 26 game between the Cardinals and White Sox.

"Nobody is speaking up for the hitters right now,” Donaldson said. “It's probably not going to be [taken] as serious as if it's a rookie or somebody else who doesn't have the time in the big leagues. I felt it was almost a responsibility for me to say something with this, that's how serious I think it is."

Donaldson said that he's had 10-15 players from opposing teams reach out in support of his speaking up about the issue, which he said he began exploring more in-depth while he was teammates with Bauer in Cleveland during the 2018 season. Bauer has long been outspoken about the potential for foreign substances to improve spin rates.

With the league reportedly intending to ramp up its enforcement against pitchers using such substances, Donaldson said he's cautiously encouraged -- but hopes to see what the results indicate over the coming months.

"I think we’re going to see it," Donaldson said. "I think time is the ultimate test, right, to where this goes. I mean, it’s been a week. We’ll see what happens. ... It's not just me. I spoke up to media, to the players' union, to MLB, to try and voice my opinion on it. To see some stuff start to go, that's good."