Bombers coach James Hird has accepted a 12-month ban, while assistant Thompson was fined $30,000 and football manager Danny Corcoran suspended for four months by the AFL on Tuesday night over their involvement.
Hird has nominated Thompson, who coached the Cats to the 2007 and 2009 premierships, as the obvious choice to replace him during his suspension.
While Thompson and the Bombers are yet to declare their hand, Cook said Thompson's willingness or otherwise wouldn't be the only consideration.
"It could be a combination of whether Essendon are willing to appoint someone who's been through this saga (and whether) the AFL have any say or influence on what happens," Cook told the Nine Network's Sunday Footy Show.
"I'm not sure they (the AFL) would be overly happy.
"I shouldn't be talking for them but that's the impression I get."
Cook predicted the League would be asking questions of the Bombers if they appointed Thompson, given he's been sanctioned.
"I think so, yeah. I don't think it sends a great message," he said.
Cook said if the same situation occurred at Geelong, he would look elsewhere for a replacement coach.
"Our reputation would have been damaged to some degree and we would have needed to claw that back," he said.
"My opinion is I would have brought some fresh people in."
Fellow Bombers assistant Simon Goodwin and Brisbane Lions assistant Mark Harvey, a former Essendon star player, are others believed to be under consideration.
But Essendon great Matthew Lloyd said Thompson would be the best choice and his association with last year's supplements program shouldn't disqualify him.
"Bomber Thompson was part of it but I don't think he was a huge part of it," Lloyd said.