Jim Jefferies insists Kilmarnock will not alter the £2million fee on Steven Naismith's head.
Rangers have had several bids for the striker rejected over the summer, while Celtic were granted permission to speak to Naismith at the start of the week.
The Scotland Under 21 international has subsequently withdrawn a transfer request after Celtic did not follow up their interest.
Kilmarnock remain hopeful of hanging on to Naismith, whose value will not change, irrespective of his form before the close of the transfer window, according to Jefferies.
"If he starts the season with us really well and impresses them, and shows that he's worth what we're looking for, then we'll never change it [the asking price] because that's not fair to any club," Jefferies told BBC Radio Scotland.
"(If there is a suitable bid) we'll let Steven know and Steven will decide if it's the right move. Right now we are absolutely delighted with the letter that we got yesterday.
"He's really focused now on helping Kilmarnock and we're really pleased about that."
The Kilmarnock boss also revealed that Rangers have not once been able to match the club's valuation of Naismith.
Jefferies added: "There's a price that we asked of every club and Rangers have made offers.
"They are quite entitled to value a player at whatever they like, there's nothing wrong with that, but never at any time have Rangers met our asking price which they've known from day one.
"Their valuation for Steven Naismith was nowhere near being accepted by Kilmarnock."