Rangers have had a second offer for Scotland striker Steven Naismith turned down by Kilmarnock.
BBC Sport understands that Rangers offered £700,000, half to be paid immediately, with the rest to follow in a year's time.
Kilmarnock, who had rejected a £400,000 bid, would have benefited further from add-ons for goals and appearances.
But the Ayrshire club dismissed those outright and are thought to be holding out for £1.5m for the 20-year-old.
Kilmarnock chairman Michael Johnston has kept manager Jim Jefferies informed of developments.
"Steven's got a three-year contract with us and we're not trying to sell him"
Jefferies told BBC Sport that Rangers' offer was still below Kilmarnock's valuation of the player.
"It (the offer) is a slight increase but still nowhere near what we're looking for - so we turned it down," said Jefferies.
"Steven's got a three-year contract with us and we're not trying to sell him.
"If we receive an offer that seems fair and we couldn't turn down we would see if Steven wanted to go - he would make the final decision.
"Until that happens, any offer we feel is unacceptable will be turned down."
Jefferies said Naismith had handled the speculation well and was committed to the Ayrshire club if a move did not materialise before the new season.
Naismith, who had a trial with Arsenal last season, has also been tracked by Celtic and several English clubs, with Bristol City going public with their interest.
But the striker, who made his Scotland debut against the Faroe Islands last month, would prefer to remain in his homeland at this stage of his career.
And he has stressed that he would rather stay at Rugby Park than be signed by one of the Old Firm clubs as a squad player.
He scored 19 goals last season and Rangers would like to re-unite him up front with former Kilmarnock team-mate Kris Boyd.
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