The Senators forward provided the update during one of two video calls arranged by the NHL on Monday, the 18th day since the League announced March 12 it would pause the season because of concerns over COVID-19.
"I think those guys are doing well," Tkachuk said. "We're a tight group so we're always in contact with one another, but I think all of us are just concerned about them and everybody impacted by it."
One player tested positive for the coronavirus March 17 and a second tested positive March 21. The name of each player has not been revealed by Ottawa.
The Senators played at the San Jose Sharks on March 7, at the Anaheim Ducks on March 10, and at the Los Angeles Kings on March 11 before NHL Commissioner Gary Bettman announced the season pause.
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Ottawa's medical team continues to monitor the players and staff while following all appropriate and professional guidelines to help ensure the health and safety of its employees and the community, according to the Senators.
"I think for myself and everyone on the team, we miss being in Ottawa and being part of the community," Tkachuk said. "I think all the families ... we kind of miss the game. For now, it's just staying safe and follow the guidelines of social distancing and being six feet away and washing your hands.
"For all the first responders, doctors and nurses who are battling this virus and, like everybody said, they've sacrificed so much. We think of them and everyone affected ... we just pray for them all."