The owner of the Clydesdale and Yorkshire banks is this weekend locked in talks with Virgin Money about an improved all-share offer to create a £4bn challenger lender.
Sky News has learnt that CYBG has tabled a revised bid in recent days which values Virgin Money at around £1.7bn.
The fresh approach, which comes ahead of a deadline on Monday evening, will confound expectations that CYBG chief executive David Duffy would sweeten his original proposal with a cash element.
Sources said on Sunday that the two sides were holding "positive discussions" and that they were likely to request a week-long extension from the Takeover Panel in order to try to reach a formal agreement.
A combination of the two companies would create a personal and SME banking group with 6m customers and a £70bn balance sheet - far ahead of any of Britain's other challenger banks.
It would also enable CYBG's advanced technology platform to be rolled out across Virgin Money's product base even as the latter continues to build its own digital banking capabilities through a partnership with a company founded by Antony Jenkins, the former Barclays chief.
CYBG initially made an offer of 1.1297 of its shares for each Virgin Money share, a proposal that would have given the latter's investors 36.5% of the combined entity.
The new approach is understood to have increased the proportion to be owned by Virgin Money shareholders to around 40%.
The revised offer has been complicated by the fact that CYBG's share price has slipped since the original proposal, while Virgin Money's has risen.
One of the issues which this weekend remains unresolved relates to the use of the Virgin name in a combined group.
CYBG has said it would "ensure that the Virgin Money brand would play a significant role" if a takeover goes ahead, with one insider saying that the parent company was "highly likely" to use the brand created by Sir Richard Branson.
Among the options being negotiated between the two boards is for the Virgin Money name to replace a substantial proportion of the retail banking products currently offered under the Clydesdale and Yorkshire brands, the insider added.
Sir Richard's Virgin Group holds a roughly 30% stake in Virgin Money, which bulked up after the financial crisis by buying the retail operations of Northern Rock in a £750m deal.
The merger talks between CYBG and Virgin Money are seen by analysts as an important test of whether a cluster of medium-sized challenger banks can consolidate sufficiently quickly to pose a substantial threat to the big five: Barclays, HSBC, Lloyds Banking Group, Royal Bank of Scotland and Santander UK.
Virgin Money, OneSavings Bank and the Nationwide building society have all been growing their market share, but in both retail and small business banking remain heavily concentrated among the major players.
Among the challengers, TSB has been hit by a crisis over its migration to a new technology platform, while the Co-op Bank continues to recover from the troubles which threatened its existence until last year.
At the close on Friday, CYBG had a market value of nearly £2.6bn, while Virgin Money was worth £1.53bn.
Deutsche Bank and Morgan Stanley are advising CYBG, while Virgin Money is being advised by Goldman Sachs.
Spokesmen for CYBG and Virgin Money both declined to comment.
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