The plan, which is being considered by the Cabinet, is aimed at persuading Europe to allow UK banks and insurers to keep trading freely in the zone.
It is feared that if Brussels chooses to end Britain’s free access to trade, many big name companies will shrink, close or move to other EU countries.
Oliver Letwin, David Cameron’s former policy chief, said it was vital that Britain was able to sell financial services across the EU.
He said: “If we have to buy this market access by making continuing contributions to EU budgets, that may well be a price worth paying, given the number of UK jobs that are involved.”
But Conor Burns, a Eurosceptic Conservative MP, said: “Leaving the EU doesn’t mean paying money into the EU.”