Around 5.4 billion Lloyds shares will be sold to institutional investors, raising about £4.2 billion for the taxpayer based on yesterday's closing share price.
UK Financial Investments, the body responsible for the government's stakes in banks, sold 6% of the bank last year and says it intends to sell another 7.5%.
Lloyds was bailed out by the Government in 2008 at the height of the financial crisis.
The share sales are part of the government's plan to return the lender fully to the private sector. It will bring down the Government's stake to 25% from 33%.
It is expected that a multi-billion-pound shares offering to members of the public will go ahead later this year.
The development came as disgraced former Co-op Bank chairman Paul Flowers said he had faced intense pressure from former Treasury minister Mark Hoban, and indirectly Chancellor George Osborne, to push through a deal for the bank to takeover around 600 branches Lloyds bank, but which ultimately fell through.
Asked how much pressure he had come under, Mr Flowers, who was arrested amid claims he bought hard drugs, said: "Considerable from the present Government, mainly from Conservatives.
"They wanted a deal. Remember that the Government was, still is, the major shareholder of that bank."