They will ask the American trucking tycoon to wire the £500,000 exclusivity fee today, and the only hope for the rival bid made by the Blue Knights consortium is an unlikely change of heart by Craig Whyte over his shares.
After another day of frantic negotiations between Brian Kennedy, who is now working with the Knights consortium, and Duff and Phelps, it is understood that Kennedy received notification last night informing him that a Company Voluntary Agreement with the creditors would be impossible to deliver, and that 11 weeks after being appointed as administrators, they still cannot provide Whyte's majority shareholding.
The Knights' offer is an initial cash payment and staged instalments totalling around £10m, but also involves removing the Rangers bond holders from the creditors pot (£7.7M) and paying all the football debts (£3M).
A Knights source said: "Our offer was equitable with Bill Miller's bid. But you cannot complete a CVA without the shares – and the administrators are saying they can't get them.
"Unless someone can get the shares from Whyte, how can you attempt a CVA process, even although the understanding is the cash offer would have been attractive to the creditors.
"It's like being asked to bid for a house, but you'll never get the title deeds.
"Our bid remains on the table and can be re-ignited if Whyte releases the shares, but does anyone expect him to do that? It now appears Bill Miller's will be favoured."
It now remains to be seen if Miller will come through on his £11.2m offer to buy the club, which involves moving the assets to a newco while leaving Rangers Football Club plc to try to agree a CVA.
Financial experts consider this a convoluted form of liquidation, and if Duff and Phelps believe the Knights' CVA offer to be unachievable, then Miller's would face the same problems, since it is understood there to be only a few pence in the pound difference between the value of the two bids to the creditors.
It is also believed Duff and Phelps have been attempting to persuade the Knights to adopt a similar 'newco' plan, but Paul Murray, a former Ibrox director, and Kennedy are adamant that they are not interested, since the club's 140-year timeline will be disrupted.
Time is of the essence, since Duff and Phelps have told Ibrox staff that there is only enough funds to run the club until the end of May, at which point the wage cut agreement with the players and coaching staff ends.
The majority of the Ibrox support has protested against Miller's plan, and the American is known to be wary about his bid being seen as a hostile takeover.
If he does not receive guarantees from the SFA and the SPL, and fans express their anger at tonight's home game against Dundee United, there is the prospect that he might walk away from negotiations.
That would then leave Rangers with no prospective buyers and in a potentially perilous situation.