As stocks in major banks with U.K. operations continued to face a battering since Britons voted to leave the European Union last week's referendum, executives say they are bracing for changes that may be required to meet client needs and keep their operations competitive.

While the banks say it is too early to make any definite decisions on the future of their U.K. operations, their immediate comments made publicly or internally to their staff signal that they are certainly in preparation mode for making changes. A few weeks prior to the referendum, Citigroup's (C - Get Report) U.K. head James Bardrick had reportedly sent a memo to its U.K. staff saying that the bank had a contingency plan in place in case of a Brexit and that efficient move of staff between EU member states was important for the bank and its clients.

Citigroup shares have dropped 3.7% in morning trading. The bank's headquarter for its Europe, the Middle East and Africa (EMEA) operations is in the U.K. They could not be reached for comment.

Meanwhile, Bank of New York Mellon (BK - Get Report) shares have dropped over 5.42% today. Its EMEA chief said it was ready for any changes that might be necessary after Brexit. 

"We have the flexibility and resources to adapt to any necessary infrastructure change which may be needed as a result of the formal U.K.-EU relationship and market access protocols negotiations," said Michael Cole-Fontayn, chairman for the EMEA region at Bank of New York Mellon in a statement. "We believe that we are strongly positioned to continue to provide services and solutions to our clients through all our European legal entities."

The bank has 5,000 staff in the U.K. and 51,200 worldwide. 

Meanwhile, Bank of America Merrill Lynch's (BAC - Get Report) EMEA president Alex Wilmot-Sitwell said that the bank is eager to respond to any changes that its clients make following Brexit. On Friday, he sent an internal note to his staff.

"Across each of our areas of business, we have many clients who will be reflecting on the changes that they will need to make in the light of the U.K.'s decision," Wilmot-Sitwell said in a note sent to his staff on Friday. "We must make sure that we are a vital contributor to that strategic dialogue and the first port of call when they are ready to transact their business."

Bank of America Merrill Lynch declined to disclose its U.K. headcount. Shares have dropped nearly 11% since Friday.

"We have already successfully completed the largest combination of two companies in financial services history," Wilmot-Sitwell said. "I am therefore very confident that, when the time comes, we will again execute our plans efficiently, clearly and successfully."

New York-based Goldman Sachs Group (GS - Get Report) declined to comment on whether they had any plans for moving its U.K. operations elsewhere in Europe. A majority of the approximately 6,000 employees in Europe are in London, according to its spokesman. The bank's shares have dropped 8.8% since Friday.

Meanwhile, Standard Chartered  (STAN) said the Brexit vote would not have an immediate impact on its operations. The London-based bank's share price have dropped 6.75% today and more than 9.75% on Friday.

"Given our capital and liquidity strength we are well positioned to weather the potential market volatility that has followed the vote to leave," the bank said. "There is no direct impact on us or our ability to serve our clients across the U.K., Europe, Asia, Africa and the Middle East."

London-based HSBC's shares have dropped 4% since Friday. In February, the bank made a decision to stay headquartered in the U.K. after a ten-month review. In a press conference at the time, HSBC group chief executive Stuart Gulliver said that a Brexit may result in 1,000 jobs in the bank's trading and banking division to move to Paris. The bank has about 45,000 employees in the U.K.

"Having our headquarters in the U.K. and our significant business in Asia Pacific delivers the best of both worlds to our stakeholders," Gulliver said in February. The U.K. and Hong Kong "are considered by the Board to be world-class financial centers with high quality regulatory regimes capable of hosting a global systemically important bank such as HSBC."

-- James Skinner and Laura Board contributed to this report.