This would help avoid a hard border, but would also limit the UK's ability to diverge from European Union regulations.
"If these disagreements persist, the transition is not a given", Barnier told a news conference in Brussels after a round of Brexit talks with British negotiators.
Barnier did not hide that he has some problem understanding UK's position on the transition period.
The EU has indicated that it wants a "status quo" transition period of just under two years and this would include free movement and full rights for EU citizens arriving in the UK.
He noted: "Our partners set out a certain number of disagreements which I regard as substantial".
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Barnier warns the European Union may not agree to a transitional period to reassure businesses and iron out difficulties if disagreements persist.
The EU's chief negotiator said there was a "very short" time for both sides to strike a deal to stop a cliff-edge on March 29th 2019.
This was a politely delivered but pointed message to Britain: you can't keep up your cake-and-eat-it approach of vowing to leave the single market and customs union while still wanting no checks at the Irish border. He referred to a tight time schedule with a looming deadline in March for an agreement on the transition period and October-November when the withdrawal agreement should be ready for ratification. It warned that businesses and banks are likely to relocate operations because Britain leaving the single market makes Japanese businesses "face difficulties".
"It is also a major issue for the European Parliament", Barnier said. "We haven't a minute to lose if we want to succeed".
Davis hit back at Barnier, adding it was "surprising" the Frenchman was "unclear" about London's position after a week of what he called intense work.
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The value of the pound to the dollar took an immediate dive after Barnier's comments, indicating the importance of a transition period to businesses in the UK.
He stated that "maintaining access to each other's markets on current terms means we will replicate the effects of the EU customs union during the implementation period".
After the latest round of talks between officials in Brussels, Mr Barnier told reporters that stumbling blocks remained.
It comes a day after May summoned cabinet ministers on an away day to resolve the differences between them. Yet at the same time, they dismissed the UK's push for reasonable safeguards to ensure our interests are protected.
Davis added: "It is not possible to have it both ways".
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