Strachan scoffed at the idea that Miller would be on his way, saying: "The transfer list thing went out in the 1970s, it doesn't happen here so it's a mysterious one.
"I hope Kenny is still here on Saturday morning. I can't see him going anywhere. I like Kenny, he has done very well for us."
Strachan also insists that there are unlikely to be any new arrivals at Celtic Park before Friday. He said: "I can't see anyone coming in although I can't guarantee it. Something fantastic might turn up but I can't see it.
"As for people going out, it's not for me to decide that. If the bid is astronomical or beneficial then we must think of that because it's a business. But I would imagine that our targets will be in January next year."