Kopech, 24, missed the entire 2019 season while recovering from Tommy John surgery but was expected to contend for a spot in Chicago's rotation this year. He has publicly discussed his anxiety and depression, which Cooper cited Saturday in an interview with the Chicago Sun-Times.
"I don't know what is going on with Michael, but I know he deals with some anxiety and depression, and my thought is, I sure hope he's OK," Cooper told the Sun-Times. "And I hope he gets to where he needs to be, where he's feeling good and wants to come back, because we will welcome him back with open arms."
Kopech also missed the start of summer camp earlier this month because of what the White Sox called a personal matter.
"Last time I saw him in spring training, he was in a great place," Cooper told the Sun-Times. "But let me put it this way: I sure hope the kid is OK. I'm concerned that he's not OK."
Kopech, who touched 100 mph during spring training this past March, has not made any public comments about his decision to opt out of the season.
The White Sox did not announce Friday whether Kopech has tested positive for COVID-19 or has been exposed to the virus, with general manager Rick Hahn saying in a statement that "reaching this decision is incredibly difficult for any competitive athlete, and our organization is understanding and supportive."
"Michael has been pretty open and available to [the media] on a lot of tough topics, but he's not in the mood to talk right now," Cooper told the Sun-Times. "When Michael is ready to talk, then you are going to get the real deal."
White Sox left-hander Carlos Rodon also expressed support for Kopech.
"It's Michael's decision, and we have no idea what's going on in his world, and as a team, we support him 100 percent," Rodon told the paper. "It's a tough loss. He's a guy who can boost our rotation or wherever he would line up in the row of arms. But looking forward to having him back next year."