Striker Kenny Miller is mulling over a move to Birmingham City after Rangers accepted an offer in the region of £700,000 from the English club.
The 31-year-old Scotland player has netted 22 club goals so far this term.
But he has stalled on a contract extension beyond June and he is free to speak with other clubs.
Rangers failed with a bid for Dundee United's David Goodwillie but, even if Miller moves, they are unlikely to be able to meet United's £1.5m valuation.
The fee from the Midlands club would also increase should they avoid relegation from the English Premier League this season.
Rangers manager Walter Smith had stated that his wish in the first instance was that Miller signed a new deal with the Glasgow side.
Failing that, he hoped to keep Scottish football's leading goal-scorer until at least the end of the current league campaign.
However, on Thursday Smith bemoaned the fact that the current financial situation at his club means that he will not be able to make any moves to strengthen his small squad without first selling a player.
On Friday it emerged that Rangers had an offer rejected by Dundee United for the Tannadice striker Goodwillie.
It is believed that the verbal offer that they submitted for the Scotland cap was approximately half of his club's estimation.
Miller arrived for his second spell at Rangers in June 2008, having first signed on at Ibrox in 2000 from Hibernian.
In the intervening seasons he had a one-year spell at Old Firm rivals Celtic, as well as stints in England with Wolves and Derby County.
The forward has already played under Birmingham boss Alex McLeish, who was Scotland manager in 2007.
So far, Miller has amassed 51 international caps, scoring 12 goals.
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