Naismith is currently with Kilmarnock in pre-season training in Italy
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Walter Smith has confirmed that Rangers have withdrawn their latest bid for Kilmarnock striker Steven Naismith.
The Ibrox club have yet to agree a fee with Killie for the SPFA Young Player of the Year and have now had four offers rejected by their SPL rivals.
"We have withdrawn our offer - we have our valuation of the player as do Kilmarnock," said Ibrox boss Smith.
"We would like to bring more new players in anyway regardless of the Naismith situation."
Smith made £2.8m Osasuna defender Carlos Cuellar his sixth signing of the summer this week, with the Spaniard joining DaMarcus Beasley, Jean-Claude Darcheville, Alan Gow, Kirk Broadfoot and Graeme Smith.
With the latest attempt to recruit Naismith stalling, the Light Blues manager is seeking to further add to the ranks before the Clydesdale Bank Premier League season commences on 4 August.
Negotiations to bring Wigan and Scotland midfielder Lee McCulloch to Rangers, meanwhile, remain "ongoing."
"We are still hopeful of getting a couple of players in before we get started, sooner rather than later I hope," added Smith, who has also been linked with a move for Hibernian's Steven Whittaker.
"The time factor is important to us for the Champions League qualification games and for the start of our own league season, which is only days after that.
"It's not an ideal world and it doesn't always go that smoothly - and I can assure you it is not going that smoothly!
"But if we have to wait to get what we are looking for, we will do so.
"We are getting there in terms of numbers but would like another couple in."
The Glasgow club's Champions League campaign begins with a second-round qualifier against FK Zeta or FBK Kaunas on 31 July.