Sir Mervyn King, at the launch of the Bank's quarterly inflation report, admitted discussions were being held in the UK on how to handle the collapse of the euro.
The Bank, the Treasury and the Financial Services Authority are contemplating the worst-case scenario, which would send shockwaves around the world.
In the report, the Bank warned of continued risk of a "disorderly" outcome for the eurozone, as part of its wider forecasts for the UK economy.
Sir Mervyn admitted that the bank could not quantify the most extreme risks from the single currency area but declared that the UK's biggest trading partner was "tearing itself apart without any obvious solution."
He said "Just kicking the can down the road is not an answer."
His comments came as the turmoil in the region continues after Greek political leaders failed to form a coalition government, forcing a new election in June.
The country could be denied further EU bailout funds if a party opposing drastic austerity measures comes to power, which could lead to Greece leaving the euro.
As Sir Mervyn spoke, investors continued their flight from risk over the crisis.
In addition to the bleeding of value in Greek equities, there has been something of a run on the country's banks as despositors move to protect themselves from a potential devaluation.
As much as 700 million euros (£569m) was reportedly withdrawn in a single day.
The jitters have crossed into Spain and Italy again as the contagion spreads - with the spread on 10 year bonds between Spain and Germany reaching a new record high earlier today.
The euro has also hit a three-and-a-half year low.
By late morning, the FTSE 100 had lost 0.9% of its value on the day - leaving it at a low for 2012 of 5389.
There were similar falls on the main stock markets in France, Germany, Italy and Spain.
Jane Foley, senior foreign exchange strategist at Rabobank, told Sky News there had been a rush towards the dollar as investors ran from risk and that the latest market moves were evidence of the damage the Greek crisis can inflict elesewhere.
She said: "Over the last two years, firewalls have been put up to try and stop some of this rot but...contagion is carrying on.
"We're very concerned that if Spain does ultimately need a bailout, it might just be too much that the eurozone can bear."