Former Labour leadership candidate Owen Smith will seek to change legislation to allow Parliament the option of holding a second EU referendum.
The Pontypridd MP said the government should be able to ask people if they are certain they want to leave Europe.
Prime Minister Theresa May has appealed the decision and the Supreme Court is set to hear the case in early December.
Mr Smith told BBC Radio Wales' Sunday Supplement programme: "I will attempt to amend the legislation such that there is an option for Parliament to put it to the country that there should be a second referendum.
"Now, it may not be possible to do that, the government may try and frame the bill in such a way as they make it impossible, but that will be my objective.
"That doesn't necessarily mean you have a second referendum, it may be that the terms that are negotiated are advantageous to Britain. It may be clear that the country as absolutely content with that.
"But if it becomes clear over the next two years that we are going to have greater economic uncertainty, that the country is going to be worse off and people aren't sanguine with the result, I think any sensible government would want to have, as an option in its armoury, the prospect of asking the question again in order to be certain."
If it loses its Supreme Court appeal over the High Court's Brexit ruling, it is expected that the government will have to publish some form of new law for MPs - and the House of Lords - to vote on.
The Prime Minister has vowed to carry out Brexit "in full" despite the ruling and said MPs should accept the referendum result.
Writing in the Sunday Telegraph, Mrs May said she was appealing against the High Court decision because there was "an important principle at stake".
She said MPs and peers who regret the referendum result "need to accept what the people decided" and called for unity on taking Brexit forward.
Labour leader Jeremy Corbyn has said his party would not allow Article 50 to go ahead unless Mrs May agreed four principles.
They include access to the single market, a commitment to EU workplace rights, guarantees on safeguarding consumers and the environment and a pledge to commit funds for any EU capital investment lost by Brexit.