The Clydesdale Bank Premier League champions had a bid for Dundee United striker Goodwillie rejected yesterday after finally acting on their long-standing interest in the 22-year-old, who signed a one-year contract extension until 2013 with Dundee United in March.

Rangers will have to dig deeper to land Goodwillie, who has also been the reported subject of interest from npower Championship side Cardiff.

A United spokesman told Press Association Sport: "We can confirm we have received a bid from Rangers for David Goodwillie.

"The bid has been rejected because it does not meet our valuation."

Hearts were understood to be mulling over a fresh approach for Wallace after rejecting a bid of £300,000 last week for the left-back, who is out of contract next summer.

Rangers boss Ally McCoist earlier this week admitted his interest in the pair.

Meanwhile, the Glasgow club expect David Healy to extend his stay at Ibrox, but the future of SPL-winning captain David Weir remains uncertain.

Northern Ireland international striker Healy endured an injury-ravaged spell at Ibrox last term but has apparently done enough to earn a new deal under McCoist.

Weir, though, may have to wait to discover if he is part of McCoist's plans for next term. The 41-year-old defender is out of contract this summer.

Coach Ian Durrant hopes Weir has a future at Ibrox.

Durrant said yesterday: "Davie is a great person about the dressing room and has been our leader for the last four years. Hopefully he and the boss can come to an agreement."