May has made the move to Hillsborough from St Johnstone after some impressive displays in Scottish football, but Owls boss Gray says expectations must stay realistic.
Gray thinks May has the potential to perform well but has challenged the rest of the squad to give him the right service.
“He’s very keen to get into the full Scotland squad and to come to England and hit the ground running,” said Gray.
“We’ve got to create chances for him. He’s got a calmness in the 18 yard box where he can pick out the corners. I’ve got every confidence he will convert them.
“I don’t think there is any pressure on Stevie. The only pressure on him will be what he puts on himself.”
Coke was Sheffield Wednesday’s match-winner in the 1-0 victory over Brighton on Saturday and he is looking forward to playing alongside May, but understands that it will be hard for the 21-year-old.
He told the Sheffield Star: “Everyone needs to give him time to bed in. He’s a young boy and I’m not sure if he has ever moved away from Scotland.
“We hope he hits the ground running but we know the Championship is a hard league. I think he’s come to the right club with good supporters. We are a family club. I think he’s going to really enjoy himself.
“He’s got a great track record and hopefully he can come here and hit the ground running. We are really happy he’s joined and we can’t wait to have him involved.”