Although the bank issued a statement describing the claims as "speculation", its ratings were placed on CreditWatch negative by Standard & Poor's.
Caja Madrid, the second largest savings bank in Spain, entered preliminary talks with five other regional institutions last week over a potential merger.
The Bank of Spain was forced to bail out Andalusian savings bank Cajasur last month and is now pushing for mergers to boost consolidation in the troubled sector, which suffered badly from the collapse of the property market.
However, analysts have questioned whether a process of mergers will have any real effect, as the savings banks have little scope for staff cuts or branch closures.
On May 24th, a report from the International Monetary Fund called for measures to bring about "far-reaching and comprehensive reform" of the Spanish economy.
By Tony Aynsley