The newspaper cited people familiar with the process as saying it was unlikely that a deal would be reached until at least the middle of the year because of the board revamp.
Lloyds chose the Co-op as its preferred bidder for the branch portfolio in December, with the aim of agreeing specific terms by the end of this month.
An overhaul of the Co-op board, which is made up of customers rather than company executives and non-executive directors, would need to satisfy the Financial Services Authority (FSA) of its ability to run a larger banking business.
The FSA wants more financial services expertise at group level if the Co-op acquired the Lloyds branches, which are expected to fetch about 1.5 billion pounds ($2.37 billion).
Its board is led by a former university fellow who also chairs the banking division.
If the deal goes through it would triple the size of the Co-op's banking arm from about 340 branches to almost 1,000.
One option the regulator is discussing with the Co-op is transforming the whole group into an FSA-regulated entity.
Alternatively, the Co-op could create a separate group board made up of senior directors.
The Co-op and LLoyds were unavailable for immediate comment.
(Reporting by Stephen Mangan; Editing by Bernard Orr)