Under the proposals, put forward by Brexit Secretary David Davis, Northern Ireland would be subject to both EU and British trading rules.
Mr Davis is also considering a 10-mile-wide trade buffer zone to allow local traders, including dairy farmers, to trade freely.
He hopes the dramatic plans would eradicate the need for any Irish border checkpoints, a major demand from EU chiefs in Brexit talks.
A senior British official today revealed Mr Davis' blueprint is "one of several ideas being discussed" as the UK prepares to leave the EU.
The radical plan is a major revision of 'maximum facilitation' customs deal, also known as max fac.
'Max fax' would involve using technology to reduce post-Brexit customs checks by monitoring goods passing through the UK.
A Whitehall insider said: "Max fac 2 is tremendously complicated, but it's at least something the Cabinet can unite around.
"Persuading the DUP and then the EU to agree to it will be a different job altogether and, let's be honest, it will be very hard work.
GETTYNorthern Ireland could be given joint EU and UK status after Brexit