Advisors to the U.K. Treasury have sounded out investors about buying shares in Royal Bank of Scotland Group PLC possibly as early as this week, as the government looks to k ick-start the privatization of the lender, according to people familiar with the matter.

The government, which owns a 78% stake in RBS, could still hold off depending on market conditions, these people said.

U.K. Financial Investments Ltd., a company set up to manage the government's bank shareholdings, has identified four other potential windows to sell at least £ 2 billion ($3.1 billion) of RBS shares between now and April, one of those people said.

Any sale will almost certainly generate a loss for the taxpayer. The U.K. government pumped in £ 45.5 billion to rescue RBS during the crisis at an average price of £ 5 per share. RBS currently trades at £ 3.40 per share. The disposal, done via an overnight book build, would likely see shares offered at a further discount to that price.

The sale would be largely symbolic as the government will retain a majority stake in RBS. The Treasury was advised in July by UKFI that it would be feasible to sell £ 25 billion of RBS shares by 2020. It is unclear what returns U.K. taxpayers will make on the money parked in RBS.

The bank is currently going through a vast restructuring which isn't set to be completed before 2019. Last week RBS warned that it wouldn't be paying dividends until at least the start of 2017 as it looks to hurdle balance sheet stress tests and settle many litigation issues. However, RBS Chief Executive Ross McEwan said that he didn't think the uncertainty around the bank would delay a government share sale.

Earlier this year the U.K. government hired investment bank Rothschild to review the pros and cons of selling RBS shares at a loss. Rothschild's report argued that the profits generated by the sale of Lloyds Banking Group PLC shares, the various fees paid by the banks to the Treasury and the revenues from running down the U.K.'s "bad bank", would offset any loss on RBS shares. A partial sale would also increase the number of shares traded in RBS, encouraging others to invest, and show the U.K. government is committed to privatizing the bank.

"Alongside the U.S., the U.K. will be one of the first countries that is able to demonstrate that it can comfortably expect to record a gain on its bank interventions," Rothschild said in a letter to the U.K. Chancellor.

Analysts say the review didn't take into consideration the cost of borrowing the funds to bail the banks out.

Write to Max Colchester at max.colchester@wsj.com

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