The terms of the banking to insurance group's original pounds 1.4bn bid may be varied to make them look more attractive to ScotAm's policyholders, but insiders played down a report over the weekend that a new offer would be as high as pounds 2.2bn.
An Abbey spokeswoman said yesterday: "Any figure given at this stage is speculative, because we haven't had full talks with ScotAm and seen the data we need."
She said she could not comment on a higher offer. "We would look at a mix of embedded value, goodwill, loans and free asset value, but we need to talk to ScotAm first and any figures are speculative, because we haven't improved our offer as yet."
At the moment, Abbey is offering pounds 400m for the goodwill of the Scottish life assurer, a sum which will essentially be passed to policyholders, and pounds 1bn for the so-called "embedded value" in the life fund. This is in effect a payment in exchange for the right to take up to 10 per cent a year of future surpluses.
The Pru's deal is more complicated, involving a loan to the life fund and the payment to policyholders of Scot Am's "free assets" - the amount it is forced to set aside under government regulations to ensure its financial strength.
The Abbey move comes as the bidding process shifts into a more serious phase, with potential offerors being asked to sign confidentiality agreements by ScotAm's merchant banking advisers at SBC Warburg early this week.
As well as Abbey and the Pru, it is thought that Fortis, a Belgian-Dutch financial conglomerate, and AMP, the Australian insurance group, are serious contenders.