Labour has said it is "ruling nothing off the table" over whether it will back Britain being part of the European Economic Area (EEA) after it quits the European Union.
Dozens of Labour peers rebelled in the House of Lords last week to support an amendment which would make EEA membership a negotiating objective for the Government.
Paul Blomfield repeatedly sidestepped questions over whether Labour would back the move when it goes before MPs in the Commons.
The shadow Brexit minister said the EEA has "problems associated with it" but refused to rule out supporting it.
He told BBC Radio 4's Today programme: "We are going to make our decision on the amendments that come back from the Lords when the Government brings the legislation back from the Lords."
"We are ruling nothing off the table," he added.
Cabinet Office minister David Lidington said the Government wanted to "demonstrate that we have thought this through" with its Brexit white paper.
He said two ministerial working groups set up by Theresa May last week to look for improvements to customs proposals could take weeks.
"The PM has asked smaller groups of ministers to go away and test out over the next days and weeks those detailed questions," he told BBC Radio 4's Today programme.
"So, for example, on the new customs partnership the questions are around to what extent does this inhibit an independent trade policy for the future and can we mitigate those impacts?"
Mr Lidington confirmed that assessments are being made on the legal risks of the customs options being considered.
He said: "What any government does is that when we are putting forward internally some ideas about relationships with other countries, new treaties, that we test the legal risks involved."