The UK is hoping to secure an agreement on any transition period by March this year, in a bid to provide some reassurance for business in the 12 months to Brexit day.
A time limit on the transition deal has not been agreed on either side of the negotiating table, but the EU is thought to favour 21 months and Theresa May two years.
Many are reluctant to tie down any such period, as the EU’s leverage would increase after Brexit day.
But officials from Hungary raised the idea of adding an extension clause to avoid the creation of a “cliff edge” scenario in the event a trade deal not be agreed.
However, the prospect was fiercely opposed by France and Germany – and many countries say they are still opposed in principe to prolonging any transition period at all.
A senior EU official said: “The interesting thing will be: is the transition period a one-off, or can it be prolonged?
“It will take a lot of money.”
Charles Grant, director of the Centre for European Reform, said: “Many EU governments recognise that the transition will need to last beyond December 2020. But it suits the European Union, like the UK, not to talk about that now.
“The UK would have to pay for single market access, which would require a new and difficult negotiation.”
Paris and Berlin are attempting to maximise their bargaining power should trade talks drag on for longer than expected.
Germany has suggested Britain’s banks gain access to the single market for financial services, but only if the UK pays into the EU.
France wants no access for British banks in a bid to lure them across to Paris.
One EU source said: “If Britain wants to trade budget contributions for access to the single market for the City, there will be many takers.”