The 39% taxpayer-owned bank is being forced to sell the branches after its bailout during the financial crisis and plans to float them on the stock market after a deal with the Co-operative Group collapsed.
The Sunday Telegraph said Lloyds has asked the EC for an extension until the end of 2015 as an original November 2013 deadline draws near. An initial public offering (IPO) of the 631 branches, dubbed Project Verde, is expected in the middle of next year, it added.
Lloyds' deal to sell the branches collapsed in April when the Co-op withdrew. The mutual was later forced to draw up a rescue plan for its banking arm to fill a £1.5 billion hole in its balance sheet.
The report said Lloyds has also asked for it to be allowed to sell the branches in the form it had agreed with the Co-op. That is likely to be crucial as the original sell-off plan agreed with Europe required it to offload a business with more than two times the £24 billion assets and liabilities settled on with the mutual. It is thought a stock market flotation of the branches could raise more than £1 billion for Lloyds.
The Verde branches have about five million customers, an estimated 9,000 employees and a 4.3% share of the current account market.
Chancellor George Osborne recently confirmed plans to sell off the Government's stake in Lloyds, likely starting with a share sale to institutions.
Royal Bank of Scotland (RBS) is also expected to ask for an extension for its deadline to sell 316 branches by the end of the year. A deal with Spanish lender Santander collapsed in October.
Lloyds declined to comment. RBS could not be reached for comment.