Trade minister Greg Hands told the Financial Times there was no geographical restriction on which trading groups Britain could join in a post-EU era.
One of Trump's first executive orders -making good on a campaign promise - was to withdraw the United States from the TPP, which had been billed as a counterweight of China's influence in the Asia Pacific region.
Following the departure of the U.S., the TPP bloc is working on a revised trade deal, the Comprehensive and Progressive Agreement for Trans-Pacific Partnership, which is expected to be agreed early this year.
The 11 current members have pledged to retain the measures to lower both non-tariff and tariff barriers to trade contained in the original agreement, which also aimed to implement a process to settle disputes between investors from the countries concerned.
The pact is being renegotiated after President Donald Trump's decision to pull the U.S. out shortly after his inauguration in January 2017, and is now called the Comprehensive and Progressive Agreement for Trans-Pacific Partnership, or CPTPP.
In November 2017, Fox accused British businesses of not being enthusiastic enough about global trade, saying Britain must "get more of our companies to think about exporting overseas".
Britain can not sign any trade agreements until after it has left the European Union, expected around March 2019. "With these kind of plurilateral relationships, there doesn't have to be any geography restriction".
A spokeswoman for the Department of International Trade said the government had not ruled out "plurilateral relationships".
The TPP, signed under former USA president Barack Obama in early 2016, is created to deepen economic ties between nations by slashing tariffs and fostering trade to boost growth.
Currently, these countries hold an 8% share of British exports, most prominently Japan. "It's a great thing for the American worker".
China is the UK's fifth largest trading partner and Britain hopes to sign a free trade pact with it once it leaves the EU. "It's all pie in the sky thinking". Michael Gove, the environment secretary, said in December that parliament would have an effective veto over any trade deal.
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