Co-op Bank has shared information on its business with multiple prospective buyers, after rival banks and financial investors expressed interest in a deal over the summer, said the people, who spoke on condition of anonymity.
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.
Smaller financial institutions have also come under closer scrutiny after a series of bank failures, even though rising interest rates have made lending more profitable.
Co-op Bank had a book value of 1.3 billion pounds ($1.6 billion) at the end of December. Listed UK banks trade on average at 60% of their book value, according to Refinitiv Eikon data and Reuters' calculations.
Despite interest from financial investors, Co-op Bank is more focused on a deal with a competitor, two people said. The company's valuation will depend on how a transaction is ultimately structured, one of them added.
Among those weighing bids are specialist lenders Shawbrook, Aldermore and Paragon Banking Group, in a move to secure access to cheaper current account deposits, two of the people said.
OSB Group may also be among those bidding, although a recent drop in its shares makes a transaction more uncertain, a fourth person familiar with the matter said.
Aldermore, OSB, Paragon and Shawbrook declined to comment.
Co-op Bank is controlled by several hedge funds who took the keys of the company in a restructuring process in 2017, as well as buyout houses Bain Capital and JC Flowers & Co.
Bain declined to comment. A spokesperson for JC Flowers did not immediately reply to a request for comment.
Reuters reported in April that the bank and its shareholders were considering strategic options, including a sale or initial public offering (IPO), with the help of Fenchurch Advisory and PJT Partners.
($1 = 0.8007 pounds)
(Reporting by Pablo Mayo Cerqueiro and Andres Gonzalez in London; Editing by Anousha Sakoui and Sharon Singleton)
By Pablo Mayo Cerqueiro and Andres Gonzalez