Coates showed Pulis the door last summer.
"It is a good move for Tony and I am pleased for him. I wish him well on a personal level, but this is a competitive game and my only interest is Stoke City," Coates told The Sentinel.
"Can he keep them up? Who can tell, I'm not in the forecasting business. We all know it's going to be tough because of their points deficit, but he gives them their best chance.
"I'm sure Tony is aware I wish him well, and that is quite genuine."
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