The banks' offer for ABN Amro is €39 (£27) per share, 13 per cent higher than Barclays', and the consortium says it is "of the clear view that their proposals are superior for ABN Amro's shareholders".
But any deal would depend upon the future of LaSalle Bank, the sale of which to the Bank of America was agreed earlier this week, with the consortium wanting it to remain part of the ABN Amro group.
"The banks believe that the potential transaction will create stronger businesses with enhanced market positions and growth prospects in each of ABN Amro's main markets," the banks said in a statement extolling their potential offer.
"This together with the greater combined scale of the banks and their proven track records of growing businesses can deliver concrete benefits to ABN Amro's shareholders, customers and employees."
The consortium said it was looking for further cooperation with ABN Amro with an eye on making a formal offer, 70 per cent of which would be cash and the remainder made up of RBS shares.
Barclays said on Monday that its agreed takeover of the Amsterdam-based bank would give the merged group a 47 million-strong customer base, predicting pre-tax profits of €3.5 billion (£2.3 billion) in the next financial year.
However, almost 13,000 staff are expected to be made redundant as a result of the merger if it were to go ahead.
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