The Herald Sun understands McKenna, who is asymptomatic, had trained in a small group with fellow defenders Adam Saad, Cale Hooker, Michael Hurley, Matt Guelfi, Jordan Ridley and Mason Redman.
The AFL had encouraged clubs not to stack their training groups with players from the same line.
But the AFL will tell Essendon it needs to play next week even if its starting back six are not available while in quarantine.