Natwest and Royal Bank of Scotland have written to business customers warning they may have to charge them to hold desposits as a result of low global interest rates.
This would signal the first time UK banks to introduce negative interest rates, the BBC reports.
The letter, sent to 1.3 million combined business and commercial customers, says: "Global interest rates remain at very low levels... this could result in us charging interest on credit balances."
Personal customers are not affected.
An RBS statement says: "We will consider any necessary action in the event of the Bank of England base rate falling below zero, but will do our utmost to protect our customers from any impacts."
Markets were expecting the Bank of England to cut the base rate earlier this month, but the central bank said this was now more likely in August.
The interest rate has been at 0.5 per cent since March 2009.