A representative for Co-op Bank declined to comment.
The sale is being closely watched as one of the first examples of long-touted consolidation among Britain's midsize lenders.
Co-op Bank had a book value of 1.3 billion pounds ($1.6 billion) at the end of December.
Despite interest from financial investors, Co-op Bank is more focused on a deal with a competitor, two people said.
Aldermore, OSB, Paragon and Shawbrook declined to comment.
Persons:
Toby Melville, Aldermore, JC Flowers, Bain, Pablo Mayo Cerqueiro, Andres Gonzalez, Anousha Sakoui, Sharon Singleton
Organizations:
Bank, REUTERS, Reuters, Paragon Banking Group, Paragon, Bain Capital, Co, Fenchurch Advisory, PJT Partners, Thomson
Locations:
London, British, Aldermore