Bulls forward Chandler Hutchison also tested positive for the coronavirus and has remained in Washington since the Bulls beat the Wizards on Thursday.
"That's gonna be the biggest thing as we go forward here is what happens with some of these guys that are unavailable and in the safety protocol," Donovan said. "What happens when they get lifted and when they have clearance and those kind of things."
Satoransky's positive test adds to the list of COVID-19 incidents within the organization. He previously missed time in December because of the mandated nine-day quarantine for having close contact with former Bulls forward Noah Vonleh, who tested positive during the preseason.
Guard Garrett Temple also tested positive in November, in addition to four members of the Bulls coaching staff who missed the game against the Indiana Pacers on Dec. 26 but returned for the following game against the Golden State Warriors.
Donovan feels that the recent positive tests aren't a result of guys being irresponsible. In Washington, players had a team meal as a group at a restaurant that was league-approved and was outside, but have continued to be hit hard.
Cases in Illinois have also been deadly with more than 16,755 deaths reported, according to the Illinois Department of Public Health.
"I think our guys have been really pretty compliant. If there has been anything they've been able to do on these road trips, it's all been league-approved as it relates to restaurants or going somewhere. I think our guys have been really, really compliant with that stuff. The thing that I can not speak to, we just finished up the holiday season," Donovan said. "I think for our guys, all of them have been very, very conscientious but a lot of times, it could be coming from family, it could be coming from outside, people getting together.
"Some of these guys have kids. Some of these kids ... maybe some schools are open, some schools are closed. It's just a lot of different ways, but I don't think are guys are being irresponsible in terms of going out and putting themselves in harm's way."