Dutch bank ABN Amro said it will open its books to a consortium led by Royal Bank of Scotland (RBS) that has made a €72 billion ($98.2 billion) bid for the bank.
ABN, which agreed earlier this week to a €65 billion buyout deal with Barclays, said RBS, Belgian-Dutch group Fortis and Spain's Santander could look at its books, subject to confidentiality agreements.
That could increase the chances ABN will be at the centre of a bidding war, as well as US unit LaSalle, which ABN agreed to sell to Bank of America for $21 billion earlier this week in a related deal.
ABN agreed to open its books after Chief Executive Rijkman Groenink spoke to the three banks last night to discuss their offer. He has not changed his view that the merger with Barclays is the "best option" for shareholders.
Mr Groenink invited rival bidders - which at the moment is only the consortium - to bid separately for LaSalle and ABN to take over the group.
Both Barclays and the consortium want to expand as the European market consolidates.