As it stands, the 11 remaining TPP countries, which include Canada, Japan and Mexico, have agreed to push forward with a TPP now known as the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP).
There has also been resistance in Australia where trade unions claimed thousands of jobs could be destroyed by the arrangement.
The British government is looking at other possibilities, the most important of which is the US.
Additionally, while Theresa May and her Brexit team can hold talks with potential trading partners before leaving, nothing concrete can be signed - and that may continue to apply during the transition period.More news: Deepika Padukone wants Ranveer Singh to quit doing this thing
And Simon Fraser, previously the most senor civil servant at the Foreign Office, tweeted: "Welcome to cloud cuckoo land".
Trade Minister Greg Hands was unable to name a single country that had expressed interest in a post-Brexit trade deal in response to a parliamentary question.
At the time of the referendum, a negotiation with TPP would have encompassed the U.S. as it was a member.
In comments published in the German newspaper Die Welt, the crossbench peer said: "Brexiteers in May's cabinet like Boris Johnson or Michael Gove were very intellectual, smart people". They are clueless, sadly. By comparison, Germany alone accounted for 11 percent.More news: Blackhawks Rout Senators, 8-2
Senior UK cabinet figures have argued internally that forecasting around trade has been too reliant on the so-called gravity model. Not only are they benefitting countries like Great Britain, but they are helping the economies of Latin America as well.
Fox told Bloomberg TPP was not the UK's top priority as it negotiates to leave the European Union but that "it would be quite wrong" to rule out a potential deal.
The proposal, being developed by Liam Fox's Department for International Trade, would make the United Kingdom the first member of the Trans-Pacific Partnership that does not border the Pacific Ocean or the South China Sea.
"In terms of viability, TPP hasn't been concluded and there is a long way to go".More news: Trump's 'S***hole' Comment May Have Won Back Ann Coulter
But Labour criticised the interest in TPP and urged ministers to look closer to home and focus on the "key future trading agreement" with the EU.