Reports show that Governor Mark Carney has told UK banks to prepare for the possibility of a rate cut, and asked whether their balance sheets could absorb a rate reduction.
A source told The Times that he had been invited to an ‘informal discussion’, with another banking boss adding that "this is something the Bank has been suggesting for some time".
The Bank publishes its inflation report this week, which is expected to contain further analysis on the implications of a Brexit.
Carney has previously said that some financial services firms would leave London if Britain left the European Union.
Discussing the economic and financial costs and benefits of UK's EU membership with the Treasury Select Committee, Carney said that "certain firms would take a view in terms of relocation".
He added that negotiations to protect the current landscape would take a long time, and that Britain would almost certainly lose influence over regulations.
Discussing the Brexit more generally, Carney said that "the situation could bring some challenges to financial stability".
