The issue flared up again on Thursday, with AFL chief executive Andrew Demetriou saying it defied belief that King was still in contact with Mitchell.
Demetriou has called on King to reconsider the friendship for his sake and that of Richmond.
Koch did not hold back when asked about Demetriou's comments.
"We'd get rid of him, absolutely," Koch told Channel Seven on Friday.
"Simple as that. Our leadership group would tear him to shreds and say either you stop doing this or you're not part of our group anymore."
Richmond have banned Mitchell from club events after King brought him into their MCG changerooms last August.
They have asked King not to associated with Mitchell, but not ordered him to end the friendship.
The pair have since been seen in public twice.
Demetriou said he had spoken to Richmond chief executive Brendon Gale about the issue.
The AFL boss said the league was within its rights to tell players not to associate with particular people.
We've spent 12 months talking about people who seek to infiltrate the game for a number of things," Demetriou said.
"I'm not suggesting for a minute it's this case, but I'm talking about match-fixing, information sharing, performance-enhancing drugs, illicit drugs - these are serious issues so we've got to do everything we can to protect it."
The AFL Players Association said there should be no blanket rules covering who players can associated with, adding it should be dealt with on a case-by-case basis.