In a tweet, Gilmore said he is asymptomatic, urged people to take the coronavirus seriously and thanked those who have reached out.
The Patriots have canceled Wednesday and Thursday practices. They are scheduled to host the Denver Broncos on Sunday at 4:25 p.m. ET.
Gilmore is the second Patriots player to test positive, along with quarterback Cam Newton. Practice squad defensive tackle Bill Murray also was placed on the reserve/COVID-19 list Tuesday. Being on the list does not mean a player has tested positive for the coronavirus; it could also mean he has been in close contact with someone who has tested positive.
The Chiefs' tests all came back negative Wednesday morning, a source told ESPN's Dan Graziano.
The Patriots took two planes to the game Monday, with a group of players who had the closest contact to Newton on one plane and the rest of the team on the other.
Gilmore was on the plane of people who had close contact with Newton, a source told ESPN.
Newton took to Twitter on Wednesday, emphasizing the importance of wearing a mask.
WEAR YOUR MASK • KEEP YOUR DISTANCE pic.twitter.com/0IBolQt3rx— Cameron 1 Newton (@CameronNewton) October 7, 2020
The Patriots have shut down their football operations at Gillette Stadium, outside of essential personnel, with plans to handle everything virtually on Wednesday and Thursday.
After Monday's game, Gilmore acknowledged how things changed for the team after Newton tested positive.
"It's just a situation we had to go through, a lot of testing," he said. "We had to adjust a lot. ... At the end of the day, we came out, fought as much as we can but just came up a little short."