But Abbey National refused to give any further details of any likely increase, beyond repeating that its original pounds 400m cash or shares offer had been a minimum figure and would almost certainly be raised above that amount.
Abbey also hoped to arrive at a more exact valuation of ScotAm's life fund which it provisionally valued at between pounds 700m and pounds 1bn late last week.
Its original bid contrasts with that of Prudential on Wednesday, which offered pounds 1.9bn, including pounds 400m in cash or shares and a further pounds 400m in bonuses to policyholders. The remaining pounds 1.1bn is the Prudential's valuation of the life fund.
Charles Toner, deputy chief executive at Abbey National, said: "[Our] offer will take account of the most recent financial information, which Scottish Amicable intends to provide to all bidders.
"Abbey National has started work with Scottish Amicable to ensure that its final offer fully values policyholders' interests as well as the interests of staff." Mr Toner added that he expected future discussions to be subject to confidentiality clauses binding on both companies.
An Abbey National spokesman added yesterday that the bank's offer was likely to involve an increase in its pounds 400m goodwill offer for ScotAm. The life fund valuation would depend on actuarial calculation.
He said, however, that when the offer was finalised prospective policyholders would have to reach a decision not simply on the basis of how much up- front money was on tap.
Also important would be whether it was better for the life fund to benefit from a direct cash injection, as Abbey was proposing, potentially enhancing long-term savers' returns, or a loan on offer from Prudential which might unlock the life fund's assets but would then close it to new business.
Abbey National's statement is the latest stage in the battle for control of ScotAm. The insurer announced proposals last month for a two-stage flotation, which would have given bonuses worth up to pounds 400m to policyholders after three to five years.
But its plans were attacked after it admitted that directors might receive share bonuses worth up to pounds 14.4m from the deal.