The 20-year-old Scotland striker has been a priority on Rangers boss Walter Smith's list of summer targets.

However an initial offer of £400,000, only half of which would have been paid up front, was thrown out by Kilmarnock and a follow-up offer has also been dismissed.

Kilmarnock manager Jim Jefferies told The Herald: "I spoke to Michael Johnston the Kilmarnock chairman and he filled me in on the discussions that have taken place. Rangers have made an improved offer but it was still not near our valuation.

"There has been talk of more than £1million with add-ons but it was not in that area.

"It was an increase on their last bid but not substantial enough for Kilmarnock to consider acceptable.

"It was also structured with half up front, and half in a year's time.

"It's up to Rangers what happens next. We have always said that unless we receive a bid that we consider acceptable then Steven will stay with Kilmarnock for next season. If the right money is put forward then it will be up to Steven what he does."