A loan to Stoke City has been rumoured for the Trinidad & Tobago international, who was taunted with chants inferring that he is lazy during the defeat at Gillingham.
John joined the Sky Blues from Birmingham in September scoring on his debut, but a couple of penalty misses and some dour performances have turned much of the City support against him.
Micky Adams was asked about the abusing of Stern John at the press conference after the Burnley defeat but chose to side-step the issue.
Dele Adebola said: "It is not very helpful. "Stern came back from international duty where he had been away for ten days and he had just stepped off a flight as well. I am not sure the manager was even going to use him because he hadn't trained with us, so it was unfair.
"I was on the end of criticism last season and it is not nice because you know at any point people can turn on you. Maybe people think it is justified, but the idea of supporters is to get behind the players, particularly considering our position.
"I think Stern's goals could be important to us at this time. He has scored six and been on a good run so he could be quite a big figure and the last thing you want is for players of his calibre not to want to be here or be perturbed by his own fans booing him."
"I have spoken to him about it but I think he understands anyway. He can only play how he plays and I don't think he was any different at Birmingham and Nottingham Forest. He is Stern John and if he changes the way he plays he won't be as effective as he has been at those other clubs. "He may need to buckle down and meet things half way but he will work it out and hopefully the fans will get behind him."