The admission follows a letter sent by trustees to the scheme's 315 members this week, in which they report a "disappointing" impasse in attempts to reach a compromise with Murray International Holdings (MIH) over the deficit.
It comes after the latest accounts for MIH show the company had a bank loan and overdraft totalling just under £351m at June 30 last year, with Sir David reporting it was nearing the end of a debt reduction strategy it has pursued with Lloyds since 2009.
In the letter, obtained by The Herald, trustee Stephen Foster at actuary Punter Southall writes: "I received a further communication from the Company on 21 May 2014, which makes clear that the Company will be unable to let me know its position until it has discussed matters with its secured creditor, Lloyds Banking Group.
"I understand that the Company expects to receive feedback from the bank on this matter in the near future.
"This development is disappointing as I had wanted to relay more positive news to you. When there is anything substantive to report I will be back in contact again."
Asked to comment on the letter, Mike McGill, group finance director at MIH, confirmed any deal with the pension trustees would require the consent of the bank.
He said: "We are continuing to work with the trustees to see if we can get a compromise agreement.
"And like any party who has borrowed money under the terms of a bank facility, any settlement of this sort of nature would require the consent of the secured lender.
"I am hopeful we will reach a sensible compromise to the benefit of all stakeholders."
The Herald revealed on May 10 that trustees at Punter Southall had been rebuffed in calls for MIH to pay the deficit in full, as it highlighted concerns over the group's "worsening financial position".
MIH had reached an agreement with trustees in April 2010, under which it committed to making payments towards funding the deficit with funds arising from asset disposals, as and when they arose, in addition to an annual sum of £1 million payable monthly.
However the company, which insists it made the first move in attempts to reach a deal over the deficit in March 2013, stopped making additional payments in September.
MIH continues to make regular payments to the scheme.
In a previous letter to members, the trustees revealed they had launched a joint bid with MIH to explore a possible buyout of the plan by specialist insurance companies.
The aim is to secure benefits for members in excess of what would be expected under the Pension Protection Fund, the pension lifeboat.
While that option remains on the table, news of Lloyds' involvement in the process has not been welcomed.
An unnamed pension scheme member said he was concerned the fund was not receiving enough benefit from recent asset sales. He said: "MIH is selling assets, fire-sale assets supposedly, to Murray Capital, the family company, at the same time as the pension is not being fulfilled.
"Were these [deals] done on competitive tender...[and] why is the money not going into the pension fund?"
Sir David hailed MIH's asset disposal and debt reduction strategy in the company's latest accounts.
During the year it raised £22m by offloading Premier Hytemp, while PPG, its commercial property arm, netted disposal proceeds of £18.1m. PPG has booked a further £104.4m of disposals since year end, and in February family-owned Murray Capital bought most of the property assets of Murray Estates for £13.9m.