Following an undisclosed number of non-binding proposals from potential bidders, the lender said its formal discussions with Coventry would enable both parties to "better evaluate the merits of a combination".
There is no certainty that the talks will result in a transaction, Co-op Bank said, adding that a further update will be provided in due course.
Co-op Bank had been working to turn around its finances and has bounced back into profit in recent years after its near-collapse and rescue by a group of U.S. hedge funds in 2017.
The lender has long been seen as a potential takeover target, as mid-sized lenders generally have struggled to gain scale to break the dominance of Britain's 'Big Four' banks - Lloyds, Barclays, NatWest and HSBC.
Reuters reported in April that Co-op Bank was exploring its strategic options.
In October, Reuters reported that private equity backed Shawbrook had tabled an indicative bid for Co-op bank.
Rival mid-sized lender Metro Bank secured a 925 million pound ($1.17 billion) refinancing package earlier this year to shore up its finances after urgent weekend talks, in a sign of the wider strains facing Britain's so-called 'challenger banks'.
($1 = 0.7926 pounds)
(Reporting by Sinead Cruise and Iain Withers, editing by Lawrence White)
