The £700m deal with US hedge funds would allow Co-Op Bank to continue as a stand-alone entity.
In a statement, Co-Op Bank said: "The Bank confirms that a majority of the key commercial aspects of the Proposal have been substantially agreed between the Bank and the Investors. Discussions are continuing between the parties, including on other key matters, with a view to agreeing the final aspects of the Proposal and a further announcement will be made in due course.
"Given the advanced nature of the Proposal, the Board has decided to discontinue the Formal Sale Process under the Takeover Code. The Bank is, therefore, no longer in an "offer period" for the purposes of the Takeover Code and, accordingly, the requirement to make disclosures under Rule 8 of the Takeover Code has now ceased."
Earlier this month, Qarati and Swiss investment groups were rumoured to be considering a takeover of the Bank.
According to Sky News, Interritus Limited and Al Faisal Holding "held several rounds of talks" with Co-op Bank, however sources said there are "a series of significant hurdles to any deal being agreed".
Virgin Money walked away from talks regarding a takeover of Co-Operative Bank in May.
