The Ibrox club confirmed on Friday they had rejected an offer for the 24-year-old, widely reported to be in the region of £2.5m, from the Coca-Cola Championship side.

However, Rangers are likely to find their resolve tested again, with City chairman Peter Ridsdale revealing the FA Cup finalists are willing to step up their attempts to secure their target.

He declined to identify Boyd but confirmed: "We are prepared to increase our offer on a player for whom we have already submitted a bid."

Despite an impressive goalscoring return since his £400,000 transfer from Kilmarnock in January 2006, Boyd has yet to earn a regular place in Walter Smith's line-up.

He faces increased competition next season following the capture of three new strikers in the shape of Kenny Miller, Andrius Velicka and Kyle Lafferty.

A move to Ninian Park could allow him to spearhead Dave Jones' attack and provide the opportunity to demonstrate his ability to perform at a high level south of the Border.

But Ridsdale warned that Cardiff would not be held to ransom in the pursuit of a player who this week reiterated his desire to remain at Ibrox and fight for his place.

He added: "It all depends on the right price at the right level. We know our price and we have other options."

Meanwhile, veteran defender David Weir is set to sign a new one-year deal with Rangers next week.

The 38-year-old held talks with Smith on Thursday after returning from holiday. His agent Dave Lockwood said: "It is very likely that Davie will sign with Rangers for another season."

Rangers are also reportedly on the trail of £2.5m-rated Czech defender Marek Suchy. The Ibrox club are keen on the 20-year-old Slavia Prague player, according to press reports in the Czech Republic.

Suchy can play in central defence or move into midfield and was voted Most Promising Player last year by UEFA after starring in the Under-20 World Cup. He is under contract until 2010 and Slavia know they can cash in on their player if they sell him this summer.

Everton were strongly linked with the player in January, but the move failed to materialise.