The group revealed that negotiations will once again proceed with the Co-operative on an exclusive basis in the hope of finalising an agreement as soon as possible.
A source suggested the main points of a deal, or heads of terms, could be agreed within weeks.
The decision was a blow for NBNK, the new bank vying with Cooperative to win control of the assets that Lloyds must sell to appease EU regulators. These include 185 Lloyds TSB Scotland branches and the Intelligent Finance internet operation.
NBNK forced its way back into contention in April with a reported £1.7 billion revised bid after talks between Lloyds and the Co-operative were delayed.
However, when Lloyds said late yesterday afternoon it had broken off talks with NBNK, the would-be consolidator concluded it had no future. Set up by former Lloyds of London insurance market chairman Lord Levene, NBNK had failed in previous attempts to buy banking assets. It had talks about buying Clydesdale Bank from National Australia Bank but did not submit a formal bid.
"The directors of NBNK have concluded there are no other UK banking assets available for sale that would meet the company's objectives and, consequently, they expect to commence steps to wind-up the company," NBNK said.
Sector watchers had expressed doubts about the Co-operative's ability to comply with the regulatory and capital requirements involved in running an organisation on the scale of the "Project Verde" units Lloyds is selling.
The Co-operative was appointed preferred bidder ahead of NBNK in December. A period of exclusive talks ended in April after the sides failed to agree a deal in time.
However, in an update on the sale process that it had promised to provide before June 30, Lloyds said: "The group and Co-op now have an understanding on the commercial terms for the transaction."
The bank added: "In order to proceed to 'Heads of Agreement', negotiations with the Co-op will proceed on an exclusive basis."
The sale now under discussion involves smaller savings and mortgage books than originally envisaged. This means the funding gap any buyer must close will be smaller.
Lloyds said the Co-operative would need to provide £1.5bn capital to support the business under discussion. A Lloyds spokeswoman declined to give any indication of the sale price it expects to achieve.
Lloyds said completion of the transaction is subject to agreeing satisfactory documentation, the approval of the company's boards, and further discussions with the Financial Services Authority, the Treasury and the European Commission.
The spokeswoman confirmed Lloyds Banking Group is still pursuing a twin-track approach that could result in it floating the Project Verde unit on the stock market.
However, she said Lloyds is confident of completing the sale by the November 2013 deadline set by the EU Commission.