The consortium, which also includes Fortis and Spain's Santander Central Hispano SA, will hold talks next week after ABN Amro came to an agreement to extend the deadline of their exclusive negotiations with Barclays, which had been due to end today.
A statement issued jointly by Barclays and ABN Amro said that the talks are "progressing, but there can be no certainty that they will lead to a transaction or the form it will take".
Barclays has now been negotiating with ABN Amro for 30 days during which the time the two banks have come to an agreement that the new venture resulting from any merger would have its headquarters in Amsterdam and listed in London.
Should the consortium's bid be successful however, it is likely it will seek to break up and sell off some of the bank's interests.
The initial approach from Barclays followed criticism of the Dutch bank's performance by activist hedge fund The Children's Investment Fund, which holds a three per cent stake in ABN Amro.