Kilmarnock have acknowledged Steven Naismith's transfer request but are refusing to agree a move until a bid of at least £2m is received.
Killie boss Jim Jefferies hopes to keep up Naismith's spirits
Chairman Michael Johnston said: "While I respect his wishes, I also have a duty to the club to make sure we get the appropriate value.
"We've looked at what has been happening in the Scottish transfer market in recent months.
"And we feel a fee in the region of £2m is not unreasonable."
The Scotland international submitted a written transfer request after becoming frustrated during the summer's long-running transfer saga.
Rangers have failed with four bids for the 20-year-old, while Hearts and Hibernian have also made contact with Kilmarnock about the player.
There is no change on that situation and that's it
Rangers manager Walter Smith
Celtic are thought to have made a fresh inquiry this week.
"Steven has been the SPL Young Player of the Year two years in a row, second top goalscorer last season, and is a full Scotland international," said Johnston after a meeting with Naismith and his agent.
"So why would you let a talent like that go for a lower figure when you see the likes of Kevin Thomson, Anthony Stokes, Lee McCulloch all in the £2m category and that leaves aside Scott Brown in the £4.4m category?"
"I had a two-hour meeting with Andrew McCormick and Steven and Steven was able to express his own views.
"I'm fully aware Steven would like to leave as he feels this is a turning point in his career and it's an opportunity to get a move to a bigger club as he sees it and get financial security.
"I can understand he feels frustrated that we're standing in his way.
"We feel we've not been unreasonable as we have not slapped a huge figure on his head to block the move.
"We haven't insisted he speaks to clubs in England, although we know that has eliminated a major proportion of the transfer market and in all probability we would get a lot more for him.
"We have respected his views and if someone matches what we feel is a fair and reasonable price then he can go.
"Steven seems more keen on a move to Rangers. He explained his concern over a move to Celtic is in relation to the strength of their squad and the number of forwards they have.
"I said if he is as good as we all think he is then he doesn't need to worry about that and he'll soon establish himself as a first-team starter at Celtic or Rangers.
"That is his concern, but he does have an open mind about Celtic."
Rangers' most recent offer of £1.5m, including add-ons, was rejected by Kilmarnock, with Johnston claiming that another club have verbally indicated that they are willing to offer more.
The Glasgow club's manager, Walter Smith, did not think that Naismith's written transfer request would lead to a fresh offer from Ibrox.
"There is no change on that situation and that's it," he said.