The 25-year-old striker is seeking a move to Liverpool and after ruling himself out of the Magpies pre-season tour of Asia with a "minor thigh injury", he has been training alone at his former club Real Scoiedad.
And though the manager is expecting the Swedish international to return to the club, he insisted he won't put up with "poor" behaviour.
He told Mail Sport: "You have to earn the right to train with us.
"We are Newcastle United. The player has a responsibility here to be part of a team and part of a squad - you have to act in the right way. So that is also at play here.
"We will make sure that any player does that to earn the right to train with the group. No player can expect to act poorly and train with the group as normal."
But Eddie admitted he "doesn't know" if Alexander will report for training later this week.
Speaking from South Korea, he said: "Of course I'd like him to be (there), but whether he will I don’t know at this moment in time.
"We have been here with the time difference, preparing for training and for games. Other people have been dealing with that situation back at home."
Liverpool have already had a £110 million bid for the player rejected and are yet to make a second approach.