Rumours emerged suggesting the Government is considering forming a new customs union with the bloc to allow tariff-free trade in goods after Brexit.
But Mr Cash said Theresa May would meet fervent criticism from Brexit voters if she failed to sever all ties with the European Union in 2019.
He said: "If you were to stay in the customs union indefinitely, of course, there would be a massive row, But that is not what is happening."
BBC
International Trade Secretary Liam Fox dismissed the claims, saying that remaining inside the EU customs union would "not be compatible" with the demands for post-Brexit trade independence.
Speaking to BBC Daily Politics, Mr Cash added that Britain will clarify the trading arrangement with Brussels as talks with the bloc resume.
He continued: "Certainly, there are very serious questions inherent in the distinction, as I would put it, between being in the customs union and a customs union.
"What a customs union means is something yet to be resolved."
If you were to stay in the customs union indefinitely there would be a massive row
Following a successful visit to China – during which the Government secured £9bn worth of deals with local businesses – the Prime Minister promised Brexit supporters she will regain full control of the economy while establishing a new trading relationship with the EU.
Mrs May said: "What I'm saying to the British people is `You voted for us to leave the European Union. That's what we will do.'
"People voted to leave the EU, but as we do that, of course, the relationship we have with the remaining 27 countries of the EU is going to be a different one from the one that we have at the moment.
"We've been very clear that we want that to be as tariff-free and frictionless as possible. But it's also important that we are able to negotiate trade deals around the rest of the world. What we're doing is looking for an arrangement with the EU which is good for the UK."