Co-op Bank was forced to put itself on the market in February after it was unable to reach a strong enough footing to satisfy Bank of England regulations.
But in June, it said it was in "advanced discussions" with a group of existing investors on recapitalisation.
Now the bank says the plan has been "substantially agreed".
The Co-op Bank, in which the Co-operative Group still has a 20% stake, was rescued from the brink of collapse by a group of hedge funds in 2013.
In a statement, the bank also said talks were continuing over the separation of its pension fund from the Co-operative Group's scheme.
Under the current arrangement, the bank must carry a share of the Co-op Group's £8bn pension liabilities, something which is proving unattractive to potential investors.
Earlier this year, it reported its fifth annual loss in a row, although the £477m deficit for 2016 was an improvement on the £610m loss recorded in 2015.
When it offered itself for sale, the Co-op Bank blamed low interest rates and the higher-than-expected cost of its turnaround plan for its failure to meet the Bank's Prudential Regulation Authority rules.
The Co-op Bank has four million customers and is well known for its ethical standpoint, which its board had said made it "a strong franchise with significant potential" to prospective buyers.
The Co-operative Bank says it is no longer up for sale, pending an announcement on fund-raising proposals aimed at safeguarding its future.