Britain will take a stake of up to 75 percent in Lloyds Banking Group
Lloyds and the UK government reached a broad agreement on the deal late in the day after a week of intense talks, the person said.
The deal could see the government's voting stake in Lloyds rise to about 60 percent from 43 percent, the person said, adding the government's economic interest could rise as high as 75 percent under the deal.
Both Lloyds and the Treasury declined to comment.
Confirmation of the deal is expected to be released on Saturday, the source said.
Lloyds would follow Royal Bank of Scotland
Lloyds has been locked in talks with the Treasury for more than a week. A delay to the deal raised concerns the talks had run into trouble, with the bank's executives keen to prevent the government taking a majority stake.
Lloyds' problems stem from its takeover of HBOS in January, which exposed the traditionally conservative Lloyds TSB to billions of losses from bad corporate loans, rising defaults on home loans and losses on toxic assets. HBOS made a 10.8 billion pound loss in 2008.
Banks will pay the government a fee for insuring the assets, and also take the first loss on the assets. For RBS, the first loss, the fee and the loss of tax benefits amounted to about 10 percent of the value of the assets.
The Wall Street Journal website said Lloyds will try to raise money from its existing shareholders with a share offer, but if they fail to take up the offer the UK will step in to buy the shares.
The government's stake will rise to 75 percent if new B shares are converted into ordinary shares at a later date, the person familiar with the matter told Reuters.
Banks using the asset plan also have to agree to increase lending to small businesses and home owners, probably for the next two years.
Analysts had expected Lloyds to put about 250 billion pounds of its riskiest assets in the insurance scheme.
The government has insured 325 billion pounds of assets owned by RBS, which could lift the state's 70 percent stake up to as much as 95 percent.
(Additional reporting by Myles Neligan; Editing by Dan Lalor, Bernard Orr)