Hibs have had a £750,000 bid rejected by Killie and Jefferies revealed: "I have read reports saying that we have gone back on an agreement with Rangers and also that we are putting too high a price on the head of a player who has yet to fulfil his potential. That is simply nonsense.
"I have been speaking to Walter Smith regularly and it has all been amicable. Rangers have their own valuation of Steven, that's fair enough, but it doesn't match ours.
"At no point have we moved the goalposts on this or tried to stir up an auction for the player.
"I don't see how anyone can suggest £2 million is an unrealistic price for a player like Steven Naismith. Never mind talking about someone with potential, he has been a top performer in the SPL for the past two years, won a string of awards, was the country's second top goalscorer last season and is now a full Scotland international.
"Of course he can still improve, but he is already an excellent player and I think I've been in this business long enough now to know what is a fair valuation in a situation like this.
"We do have a better offer in for Steven now from a club who do not wish to be named. If they come back to us, which we expect them to, with a firm bid which takes it to our valuation, then it will be up to Steven whether he wishes to speak to them.
"Steven knows that what we are asking for him is reasonable. He has three years left on his contract with Kilmarnock and we are not desperate to sell him. He has handled the whole situation superbly well.
"He may be disappointed that Rangers have not been successful with their bids for him, because they are a big club who could offer him European football and higher wages than we can.
"He wants this to be resolved one way or the other, to know where he will be playing his football at the start of the season, but he understands that we will not consider selling him unless our valuation of him is met."