Lloyds Banking Group has called for first bids for the 632 branches it has put up for sale to be delivered by the end of Monday, it has been reported.
The taxpayer backed bank aims to identify a preferred bidder by November at the latest, the Mail on Sunday said, possibly before the Independent Commission on Banking delivers its report on the industry on September 12.
Lloyds is being forced to sell the branches by the European Union in return for up to £20 billion in state aid following the October 2008 bailout of the banking sector.
Virgin Money has expressed an interest in both Lloyds and Northern Rock, which the Government is looking to sell.
Fledgling group NBNK, led by former Northern Rock boss Gary Hoffman, is also expected to table an offer for Lloyds, but has said it is not interested in Northern Rock.
The Co-operative Group is also expected to make an offer - acquiring the branches would see Co-operative Financial Services expand to more than 1,000 branches.
Lloyds chief executive Antonio Horta-Osorio last month pledged to speed up the process of selling the branches in a move to make his mark on the bank after taking the top post in March.
In his strategic review, Mr Horta-Osorio unveiled 15,000 job cuts by 2014, plans to revitalise the Halifax brand and reduce its international presence.
Outside the EU commitment, the Portugese-born banker said he would keep branch numbers at the same levels.
Lloyds Banking Group has 104,000 full-time staff worldwide. In the UK, it has main offices in London, Cardiff, Edinburgh and Belfast among others.