"The laddie says himself that if anyone comes in, the gaffer will let him know. And if no one comes in, he's happy being a Kilmarnock player.
"We don't particularly need to sell him. It's not like the situation we were in a couple of years ago. We are heading in the right direction financially and I would like to keep Naismith a while longer.
"But if we get what we consider to be a fair and reasonable offer for him, we will let Steven speak with the interested club and then it will be up to him.
"He's already shown in the past 48 hours that he has got his head round the situation. The way he has handled the speculation has been brilliant.
"He's right to hope that if anything is going to happen, then it happens quickly because it is in no one's interest for it to drag on.
"He's a young boy but he's mature enough to realise that it will happen for him some day, even if nothing happens this summer.
"He's got that belief in his ability.
"If people want him instantly, they know what to do - pick up the phone and make an offer that is in line with his talent.
"We have said we won't hold him back and we will allow him to speak to clubs but we are not going to do it if they make insulting offers."
Meanwhile, Killie are hoping to tie up Clyde midfielder Craig Bryson in the next few days but Jefferies insisted reports linking him with Dunfermline midfielder Gary Mason are wide of the mark.
He added: "Mason is a good player but I don't know where the story has come from. I haven't made any enquiries and I am well covered in the midfield area.
"I don't know if it's an agent trying to create interest in the boy but I haven't spoken with Dunfermline."