KANSAS CITY, Mo. -- Patrick Mahomes called it "a little bit of a mental lapse" that he got close to Stephon Gilmore after Monday night's game between the Kansas City Chiefs and New England Patriots. Gilmore later tested positive for COVID-19.

"I was just trying to show respect to a great football player who I hope is getting better very quickly," Mahomes said Wednesday. "I'll just try to keep away from that and try not to do it again."

Gilmore said in a tweet Wednesday that he is currently asymptomatic.

"I've followed every protocol, yet it happened to me," he said. "Please be sure to take this seriously."

The Chiefs last week had a practice squad quarterback, Jordan Ta'amu, test positive for COVID-19. Mahomes said he was able to stay at least 6 feet away from Ta'amu in meetings, which he said Ta'amu sometimes attended virtually.

Mahomes still slept in a bedroom apart from his pregnant fiancée, Brittany Matthews, for the first couple of nights -- until results of his own tests came back negative.

"I've just tried to do my part to kind of keep myself away from her and social distance whenever stuff like this arises," he said. "It's something I think about every day. You have to think about that with her being pregnant, kind of that high-risk category. I just try to do my best, especially after finding out Jordan was positive."

Since the start of training camp, the Chiefs have had some players occasionally attend meetings virtually, as Mahomes said Ta'amu sometimes did. They have eliminated the cafeteria at their practice and training facility, turning the space into a meeting room for their offensive linemen. They use their indoor practice field as a space for team meetings.

"After meetings, it looks like an Indy crew coming through ... changing the tires, putting tables away and chairs away and everything else," coach Andy Reid said.

The positive tests for Gilmore and Ta'amu appear to have the attention of wide receiver Tyreek Hill, who said he was wearing face protection in addition to a face mask in an effort to avoid contracting the virus.

"I've got the Coach Reid visor going today," he said.

The Chiefs are scheduled to play the Las Vegas Raiders on Sunday at Arrowhead Stadium. The Raiders recently had a player, defensive tackle Maurice Hurst, test positive for COVID-19, a league source told ESPN's Dianna Russini.

"We take it day by day, and we try to do the best we possibly can at keeping ourselves as clean as we can and at the same time learn every day," Reid said. "We're all wearing masks. We've been doing that. ... We try to keep our nose and our mouth covered as best we possibly can and then try to be as safe as we can off the field.

"Every day is a new experience that you've kind of got to work through, and that's what we're doing."