The government says it will propose an "innovative and untested approach" to customs checks as part of its Brexit negotiations, BBC reports.
The model, one of two being put forward in a newly-published paper, would mean customs checks would not be needed at UK-EU borders.
But "robust" enforcement would be required to avoid the UK being used to bypass EU border rules.
A key EU figure said the idea of "invisible borders" was a "fantasy".
On Twitter, Guy Verhofstadt, the European Parliament's negotiator, added that other issues had to be agreed before negotiations on trade could begin.
The UK has already said it will leave the customs union - the EU's tariff-free trading area - after Brexit, and businesses have calling for clarity on what the replacement system will involve.