Murray International Holdings, chaired by Sir David, has been approached by the trustees to pay off the £22.5m deficit, having stopped making additional payments to fund it in September.
The pension scheme has 315 members, including 75 pensioners. Some 240 are members whose pensions have yet to come into payment.
MIH insisted it is "not denying the scheme is an issue for the group" and declared that it has been "engaged with the trustees to try to find a compromise solution" since March 2013.
Mike McGill, group finance director at MIH, said: "We are not sitting here in abject denial. We are aware it is an issue and we are actively managing our way through it.
"We are not unlike other corporates with [issues] over legacy defined pension schemes."
A deal struck in April 2010 had seen MIH agree to fund the deficit by £1m a year through monthly contributions while making further payments arising from asset disposals as they occurred.
The company stopped making additional payments in the third quarter of last year.
In a letter to pension fund members seen by The Herald, trustee Stephen Foster at actuaries Punter Southall states that concern over the group's "worsening financial position" has led to pursue a possible buyout of the plan with specialist insurance firms.
Mr Foster states in the letter that the trustees agreed earlier this year to a company proposal to "jointly explore a route, financed by a lower and unquantified company contribution, by which the benefits to be provided by the plan would be scaled back but would exceed the lower benefits provided by the Pension Protection Fund (PPF)".
The aim would be to recover as many of the benefits from the plan as possible on behalf of its members.
With the agreement of MIH, Mr Foster confirmed that two companies have offered to provide quotations. These quotes are expected to be discussed when the trustees and MIH meet next week.
In the letter, dated April 24, Mr Foster said: "The extent of the "scaling back" of benefits remains to be agreed but the company's position is that, with so few asset disposals remaining, they will not be able to make a substantial contribution".
Mr McGill said MIH has made "substantial payments" of around £10m into the scheme since between regular contributions, which it continues to make, and contributions arising from asset disposals.
And he declared that the letter from the trustees to the pension fund members "omits the fact the company has been engaged since March 2013 to try to find a solution".
Noting that it was MIH which had appointed the independent trustee, he said: "We are still engaged in these discussions with the trustees.
"We also involved the pension regulator to fund the best outcome."
Asked why the pension fund was in deficit, Mr McGill highlighted the fact people are living longer and bond yields being at an "all-time" low in the UK.
In the company's most recent accounts, MIH hailed the progress made by its asset disposal and debt reduction plan in the year ended June 30, 2013.
The company reduced its debt pile by £23.3m over the year, however net debt stood at £346.7m at the end of the accounting period.
It raised £22m by offloading its Premier Hytemp oil and gas business in November 2012, while PPG, its commercial and industrial property division, netted disposal proceeds of £18.1m. PPG has booked a further £104.4m of disposals since year end.
The accounts were filed shortly after MIH sold the majority of its assets held by Murray Estates, its residential property arm, to Murray Capital for £13.9m.
Writing in the accounts, Sir David highlighted the progress on disposals and debt reduction as a "significant and a very credible performance".
But in notes to the financial statements, the board and shareholders reveal uncertainty over continuing bank funding and the group's liability to a staff pension and life assurance plan cast "significant doubt upon the company's ability to continue as a going concern".