Chinese state-backed investors are eying a stake in one of the domestically focused U.K. banks, and have hired lawyers at Norton Rose Fulbright in London to examine their options for gaining a foothold in the U.K. market, sources have told CNBC.
A source close to the situation told CNBC that they had favored the Co-operative Bank, but recent publicity around its difficulties, after its former chairman Paul Flowers was exposed buying cocaine and major bondholder Aurelius sold its stake, has put them off.
The Co-op Bank is owned by its parent Co-op Group and a group of hedge funds who bought up its bonds forced it into are structure of its debt earlier this year.
(Read more: Co-op chairman arrested)
One option is for the Industrial and Commercial Bank of China (ICBC) to buy all or part of one of the struggling U.K. banks.
The Treasury is believed to have put forward the possibility of a stake in RBS. Chancellor of the Exchequer George Osborne has already moved to make London a key hub for renminbi trading and even to allow Chinese banks to open up wholesale branches in the U.K.
(Read more: The battle to be the centre of renminbi trading)
Any agreement will not be ready in time for Prime Minister David Cameron's trip to China this week,but could be announced early next year, according to one source close to the Chinese, who added that there was no certainty a deal would be made.
(Read more: China charm offensive raises eyebrows in UK)
The U.K. government still owns 82 percent of RBS and 32.7 percent of Lloyds' shares, after bailing out both banks during the credit crisis. It sold off part of its Lloyds stake earlier this year, making a £61 million ($99.6 million) profit. Meanwhile, RBS's share price has fallen by around 9 percent this month after announcing that it will create an internal "bad bank" of its riskiest assets.
"When these stakes are sold, our responsibility is to get the best price for them," a source with knowledge of U.K. government thinking told CNBC.
The U.K.-China thaw is partly because there is now more Chinese money to be invested internationally, after a pick-up in credit following a mini-stimulus program announced by the Beijing government in July. Plus, the U.K. economy is starting to pick up, with London's safe haven status and the relatively weak pound helping to stimulate investment.
Mike Trippitt, banks analyst at Numis Securities, said that any investor able to take a two-to-three year view of the primarily domestic U.K. banks would be "extremely interested" in them.
"There's definitely value in RBS shares. Lloyds also have a bit of upside, but the valuation is reasonably full. Barclays' gross leverage is still an issue," he told CNBC.
(Read more: UK banking bonuses up again)
U.K. Financial Investments, the body which manages the government stake sale for Lloyds and RBS, declined to comment, as did the Treasury.
Chinese investment in the U.K. dropped off after Cameron's well-publicized meeting with the Dalai Lama last year. However, a series of Chinese-U.K. deals have been announced in the past couple of months, despite concerns about previous investments. These include ICBC's investment in a £650 million ($1 billion) business park near Manchester Airport and a high-profile investment by China General Nuclear Power Group in a new nuclear power station in southwest England.
(Read more: Yuan moves one step closer to global currency status)
A Barclays spokeswoman told CNBC that the bank would not comment on speculation. The Co-op and Lloyds also declined to comment and RBS and Norton Rose Fulbright had not returned calls by the time of publication.
- By CNBC's Catherine Boyle. Twitter: @cboylecnbc.