The Spanish-owned group saw a deal to buy 316 branches from Royal Bank of Scotland collapse last year. It is said executives in London and Madrid have been weighing up a bid for Clydesdale for several months.
A Santander UK spokesman said yesterday the bank's focus remains "organic growth".
Clydesdale's parent National Australia Bank has previously looked at selling its UK operations, but was unable to find a buyer willing to meet the asking price.
NAB has implemented a turnaround plan at Clydesdale which will see around 1400 jobs cut by the end of 2015 and a portfolio of bad commercial property loans moved onto the parent company's balance sheet.
Last week, Credit Suisse analysts suggested NAB could enhance its stock market value through a flotation of its UK business.