The Labour leader allegedly made the comment in a meeting with Michel Barnier earlier this week.
It was recorded in an EU memo and reported in Friday’s Daily Telegraph.
But a spokesperson for Mr Corbyn talked down the claim.
We have been clear all the way through that you can’t be in the customs union if you are not in the EU.
All member states are by default part of the EU’s customs union.
That is the system which permits goods trading without customs checks inside the bloc.
In exchange, countries agree universal tariffs being on goods being imported from outside the EU.
But Labour wants the current terms of the customs union to be replicated during the transition period.
And it is leaving the door open on forming a new customs union with the EU in the future
In contrast, Prime Minister Theresa May earlier this week ruled out the UK joining any form of customs union with the EU after Brexit.
Mr Barnier is due to give a media conference on this week’s technical negotiations later on Friday.