Lloyds Banking Group Plc, the U.K. bank which has the government as its largest shareholder, will probably decide by Oct. 23 whether to proceed with a rights offering, two people familiar with the plan said.

Lloyds may seek about 10 billion pounds ($16 billion) in the share sale, said the people, who declined to be identified because the plans are private. A final decision on the size of the sale has yet to be made, said the people. Separately, the bank may also pursue a sale of Clerical Medical, a provider of investment products and pensions, and an initial public offering of Scottish Widows, one of the people said.

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