The Rugby Park manager was unhappy when the player failed to inform him that he had left the country to play a trial match for Russian club Spartak Nalchik, where he suffered a groin strain which kept him out of the defeat at Hibernian on Saturday. But he wants Kyle to remain next season.
"Kyle had been given permission to go but I was annoyed at him for not letting me know he was away," said Calderwood. "He could have sent me a text message or something but I have cleared the air with him.
"He is at hospital this morning and we will see how the damage is but we expect him to be okay for Saturday. I talked to the chairman and told him that I think he should offer him a new contract and I think that's what he is going to do.
"Kevin has been looking a lot fitter and in the last few weeks he was coming into form and most teams in Scotland would love to have him in their team.
"I have spoken to him and I think it was a bit of a shock to him going over there. He told me that he realises what he has in Scotland and what he had in England, so I don't think playing abroad is for him.
"So it is up to the chairman to sort out the finances but I don't think Kevin is against staying at Kilmarnock, especially if we can get players in that we want to get in. It is not always about money but it is easy for me to say that. He has to look after himself and his family but happiness is a big thing in football and in life."