Miller was sacked over the weekend and the club has already begun the search for a replacement.
Wallace said the emphasis was on getting the right person for the job, not necessarily a Richmond person, or even a football person.
"You just want the right person, don't you? I don't think it matter whether that person comes from outside football or inside football if they're the right person," he said.
"If you think you can get somebody to fulfil what the club needs at the time, I'm happy to work with either.
"I don't really subscribe to the fact that that's necessarily the case (the need for a Richmond person) – I reckon that what you do is you look for the right person, and if the right person is a Richmond person, well that's absolutely fantastic, because the more you can have Richmond united, I think that's wonderful.
"But you don't get a Richmond person for the sake that it's a Richmond person if it's not the right person."
Wallace admitted the timing was not great, but said the future was the focus, not the past.
"Obviously, no-one wants change, We've cried out for stability for some time in relation to the footy division, but decisions have been made and they're board decisions, and as a senior executive of the football club, you abide by the decisions that are made and get on with life.
"That's your role and responsibility.
"It's not my decision – it had nothing to do with me, I wasn't consulted in regards to it.
"Certainly I had a good working relationship with Greg, and see him as a friend – I didn't know him prior to getting here, but see him that way – but I only want good for him.
"I think he's a great footy person and think that he'd be a great acquisition for another footy club.
"But we've just got to get on with the job at hand of being involved with the Richmond footy club, and getting the best for the Richmond footy club that we possibly can."
