Morgan has opted to play an entire season of IPL with the Kolkata Knight Riders and national selector Miller claimed that the choice meant the 26-year-old had no chance of being included in the squad to face New Zealand.
"Eoin has effectively ruled himself out of contention," Miller said. "He has made the decision to stay out there.
"That's fine and he appreciates what that means for Test selection. Now he has got to show that he's better than other players who might be ahead of him, who are on duty for the Lions.
"We're happy to say, 'Right, if that's what you want to do, you want to stay out there, you can stay there'. But if you want to get back, you've got to prove your worth. He needs big runs for Middlesex."
Morgan has played 16 Tests for England.