According to Ed Davey, the leader of the Liberal Democrats, the UK should negotiate a new customs union agreement with the EU.
He will make the case in a speech on Thursday that it is necessary to strengthen Britain's economy and give it a stronger position to handle the incoming Donald Trump administration.
According to a Lib Dem source who spoke to the BBC, the strategy is a practical attempt to "turbocharge" the economy rather than a step towards EU membership.
Countries in a customs union agree not to impose charges - known as tariffs - or custom checks on each other's goods but under EU rules they can not strike their own trade deals either.
Prime Minister Sir Keir Starmer has called for a reset in relations with Brussels, but has ruled out rejoining the customs union or the EU's single market - which guarantees the free movement of goods, capital, services and people within it.
A government spokesperson said the UK wanted "to tackle barriers to help drive investment and growth" but added: "We will not re-open the divisions of the past and there will be no return to the customs union, the single market or freedom of movement."
Sir Ed's speech is his first to focus on relations with Brussels since he became Liberal Democrat leader following the 2019 general election, when the party's campaign to stop Brexit saw it slump to just 11 MPs.
At last year's general election, the party gained a record 72 seats on the back of a campaign that barely mentioned the EU at all, even though rejoining the bloc remains the party's long-term aim.
Sir Ed's call to rejoin the EU customs union is not ideological, party sources say, but about putting the UK in the best possible position to deal with the new Trump administration and the EU.
Trump has threatened to impose tariffs on US imports after he returns to the White House next week, sparking anxiety in many countries that rely on exports.
Sir Ed will attack the government for rejecting a new customs union with the EU, saying it would be the best way to tear down trade barriers and "turbocharge our economy in the medium and long term".
He will urge ministers to negotiate a deal with the EU this year, with the aim of forming a fresh customs union by 2030, arguing this will allow the UK to "deal with President Trump from a position of strength, not weakness".
In his speech, the Lib Dem leader will argue the UK needs to be far more ambitious and to act with far more urgency, "not just tinkering around the edges of the botched deal the Conservatives signed four years ago".
There are no tariffs or other barriers to trade between countries in the EU customs union - which the UK left in January 2021 when Brexit took effect.
But member countries impose common tariffs on all goods entering the union from outside.
Sir Ed is also expected to accuse Conservative leader Kemi Badenoch of wanting to go "cap in hand" to President-elect Trump and "beg for whatever trade deal he'll give us".
He is expected to describe Reform UK leader Nigel Farage as "fawning over Trump and licking his boots", and being "more interested in advancing Trump's agenda over here than the UK's interests over there".
"If we seem as weak or as desperate as the Conservatives or Reform would have us appear, Trump will treat the UK the same way he has treated so many throughout his career", Sir Ed will argue.
The UK's trading relationships with its European neighbours, or other partners such as Canada and India, can be strengthened "so much faster", he will say.
The Conservative Party and Reform UK have been contacted for their response to Sir Ed's comments.
In a speech she will deliver on Thursday aimed at rebuilding trust in the Conservatives, Badenoch will admit her party made mistakes while in power - including on Europe.