Yorkshire Building Society has said it is in merger talks with Norwich and Peterborough Building Society.
Bradford-based Yorkshire is the second-largest building society in the UK with some 2.6 million members.
The society's assets are worth some £30bn ($48.5bn).
During the past couple of years, Yorkshire has merged with Barnsley Building Society and Chelsea Building Society.
"Yorkshire has consistently said that it would consider mergers with smaller societies if these can be completed on a basis that would be in the long term interests of its current and future members," it said in a statement.
Mergers between building societies have become commonplace in recent years, with many having been converted into banks.