ING Group, BNP Paribas and Bahrain-based Arab Banking Corp (ABC) have submitted bids to buy HSBC's Turkish business, according to sources.
It was suggested the bids are non-binding, meaning the process could still take some time to complete, but that one-to-one talks have begun.
HSBC's Turkish business comprises corporate and investment banking operations as well as a loss-making retail arm.
Qatar National Bank was also interested but has not submitted a bid, one source said.
HSBC, ING, BNP and QNB declined to comment and ABC could not be reached for immediate comment.
In February HSBC chief executive Stuart Gulliver said that businesses in Turkey, Brazil, Mexico and the United States needed to improve or be sold.
The bank has started auctions to sell operations in Turkey and Brazil and is expected to restructure in Mexico and the United States.
HSBC had $8.6 billion of loans in Turkey at the end of 2014, but it does not disclose their book value, which is the value at which assets are carried on the balance sheet.
The business could be sold at about book value, meaning HSBC would not see a gain or loss on the sale, sources said.
One said the price would depend on the structure of the deal, such as whether HSBC provides financing.
An acquisition would mark a return to the takeover trail for ING, which expanded internationally with a series of deals over two decades before needing rescuing by the Dutch government in 2008.
European Union rules on state aid meant it had to sell businesses and was not allowed to make acquisitions, but the block on purchases ended this week when it cut its holding in insurance arm NN Group to 42 per cent.
ING already runs a retail bank in Turkey, but it lacks scale and needs to expand to survive in the country's highly competitive banking system.
Chief executive and chairman Ralph Hamers told analysts this month he would consider acquisitions to increase ING's presence in countries where it already has a foothold.
France's BNP also has a sizeable business in Turkey and may be keen to add scale.
BNP has made acquisitions before and after the financial crisis, but its appetite for deals has diminished since its capital strength was dented by a record $9 billion fine from US authorities last year for violating sanctions. It has said its focus is on organic growth but would consider "bolt-on" acquisitions.
ABC has gone through significant management changes in the past 18 months and is growing quickly, but HSBC Turkey would represent a big deal for a bank of its size.
Mr Gulliver is trying to cut costs and reduce complexity and is due to provide a strategy update on June 9, when he will be keen to show some big disposals are well advanced.
HSBC lost $64 million in Turkey last year, dragged down by a $155 million loss at its retail business after regulatory changes capped interest rates on credit cards and overdrafts.
It is the 13th-largest branch network in Turkey with nearly 300 sites, well behind Isbank, Garanti Bank and some state-run lenders.
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