Senior banking executives have told the BBC they expect the sector to be "on the menu" when the chancellor announces his Budget in two weeks' time.
John Healey has described the banks as part of "the crown jewels" of the UK economy, yet has refused to rule out a raid on the sector.
The biggest four banks collectively made around £15bn profit in the first six months of this year, leading to calls from trade unions and others for additional taxes.
However, the banking sector trade body, UK Finance, warned that "further increases in bank taxes would weaken competitiveness, discourage investment and job creation, and work against the government's ambition to deliver growth in every postcode".
The UK's biggest banks and building societies currently pay a surcharge of 3% on top of the baseline 25% rate of corporation tax, plus a levy on the assets held on their balance sheets.