Lloyds Banking Group shares have jumped to a two and a half year high as overseas investors stepped up their interest in buying part of the bank.

Some media reports suggested that the overseas investors may want half of the British government's stake.

Former Standard Chartered chief executive Mervyn Davies is talking to others about forming a consortium to be an "anchor" or cornerstone investor in part-nationalised Lloyds, which the government is planning to sell, a person familiar with the matter said.

Davies is a partner at US private equity firm Corsair Capital. It was too early to say how big a stake any consortium might want, the source said.

Reports said that a Corsair-led consortium of sovereign wealth funds and financial firms could buy up to £10 billion sterling of Lloyds, or half the government's 39% stake.

The UK government has received a number of tentative enquiries about the sale, including from overseas investors, a person familiar with the matter said over the weekend. The government is keen to start selling its £20 billion holding in Lloyds this year, and dozens of top investment banks will pitch for the job of handling the sale by a Treasury deadline today.

The Sunday Times said Singapore state investor Temasek had made an approach about buying a £4.5 billion take in Lloyds, although industry sources said there had been no direct approach to the UK government.

Britain's finance minister George Osborne last month gave the green light to starting the sale of Lloyds shares soon.

Lloyds shares have jumped more than 40% in the last three months, valuing the bank at about $70 billion.

They closed 3.8% higher this evening at 67.1p, well above the price the British government feels is needed to ensure it breaks-even with its stake.

Shares in Royal Bank of Scotland, which is 81% owned by the UK government, also rallied on signs of greater interest in the state-backed banks. But bankers and analysts say a sale of Britain's stake in RBS is unlikely to occur until well into 2014 at the earliest.