UK-based financial services firms are set to lose passporting rights at the end of the transition period on 31 December 2020.
The freeport idea was first raised by Prime Minister Boris Johnson during his campaign to become Conservative leader, according to the English newspaper The Guardian.
But speaking in the European Parliament, Ms von der Leyen said both models fell short of a deal which would meet the goals of allowing trade without tariffs and quotas.
The EU's chief Brexit negotiator, Michel Barnier, went further than Ms von der Leyen, warning the United Kingdom to have "no illusion" about the future of its financial services sector, which makes up 6.9% of United Kingdom economic output.
"There will not be general, open-ended, ongoing equivalence in financial services", he said.
The British Retail Consortium (BRC) said the Government would have to move fast to get infrastructure in place for the start of 2021, warning that without adequate preparations the availability of goods on shelves would be disrupted, with fresh fruit and vegetables especially vulnerable.
He also said "there will be differences" between future British financial regulations and European Union ones - though he repeated a desire for regulatory "equivalence" under which British financial firms would be deemed compatible enough to maintain access to the European Union market.
But Brussels' chief negotiator Michel Barnier said: "Wherever possible we will grant equivalence on particular sectors of the financial industry. We can decide to settle for less, but I personally believe we should be more ambitious".
Von der Leyen insisted that the 27-nation European Union is offering Britain "something we have never offered before to anybody else" on the condition that the former European Union nation guarantees fair competition and protections for workers and the environment.
"But in fact, we just are in the moment where we are agreeing with Australia that we must end this situation and we work in a trade deal with them".
"Brexit can not be business as usual", he told the MEPs.
But since then, Mr Johnson has dialled back on that scope and his government has signalled it is willing to accept trade friction as the cost of exercising sovereignty.
The European Union will only offer Britain unique access to its vast single market if the United Kingdom agrees to stick to the bloc's standards, European Commission President Ursula von der Leyen said Tuesday, dismissing British Prime Minister Boris Johnson's idea of brokering a loose trade deal with the EU.
Mutual trade ambition and a suitable agreement would "trigger an upward dynamic competiton" that would benefit both parties, she said, before handing the floor over to European lawmakers.
"I expect that the post-Brexit trade negotiations will continue to weigh on Britain, a country with one of the largest current account deficits in the world", said Marshall Gittler, head of investment research for BDSwiss Group.