McKenna returned a positive result on Saturday, forcing Sunday's planned Essendon-Melbourne at the MCG to be postponed indefinitely.

The club's immediate playing future - including scheduled matches against Carlton (June 27) and Collingwood (July 3) in the next fortnight - is uncertain.

The Department of Health and Human Services (DHHS) will advise "close contacts" of McKenna to go into quarantine for two weeks, but an investigation might not be completed until Tuesday.

Essendon chief executive Xavier Campbell said the club will give the DHHS as much information as possible about McKenna's movements.

"The main (training) session (on Friday) will be where most of the focus will be," he told 3AW.

"We've spent an enormous amount of time going through all of the data, all the detail and all that footage is being analysed right now.

"That information will be supplied to them (DHHS) later (on Sunday) and it will take between 24 and 48 hours for them to go through and analyse it to help determine who the close contacts are."

AFL legal counsel Andrew Dillon hopes a decision on which Essendon players would be required to quarantine will be reached imminently.

"There is a definition for close contact and it's if you are face-to-face for more than 15 minutes or confined space for more than two hours," Dillon told 3AW.

"What we are doing with Essendon and working with the department on is saying how does that definition apply in an Essendon training circumstance."

News Corp reported that McKenna had trained in a small group with Adam Saad, Cale Hooker, Michael Hurley, Matt Guelfi, Jordan Ridley and Mason Redman.

It could mean the Bombers are left without a group of their best defenders for the next fortnight.

But Dillon said AFL rules are "pretty clear" on clubs playing matches while players are in quarantine.

"As long as we have 22 players and a couple of emergencies you are able to have a team," Dillon said.

"So as far as the AFL (is concerned), we have enough players to fill a team with a couple of emergencies we are ready to go."

McKenna's attendance at an open house inspection is reportedly at the centre of an AFL investigation to determine how the Irish defender, who is asymptomatic, contracted the virus.

The 24-year-old faces a suspension if he is found to have broken strict protocols to attend the inspection.

Australian Associated Press