Labour are already making plans to boost relations with Brussels by attending EU foreign affairs meetings, if they win the next general election.
Sources close to Labour suggested they wanted to build a more structured dialogue with the EU, should they form the next government.
Officials pointed to US Secretary of State Anthony Blinken as one example of a non-foreign minister who has attended past meetings in Brussels.
Party sources told The Telegraph they would speak to the bloc about establishing occasional access to the forum but would not be seeking ad-hoc membership or voting rights.
Keir Starmer could create closer ties with the EU
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Labour sources stressed they are not wedded to the idea of attending such meetings in Brussels, but saw them as a way of establishing a better dialogue between the UK and the EU.
Shadow foreign secretary David Lammy has laid out Labour’s plan in Foreign Affairs magazine for "progressive realism" on the global stage as the US shifts its focus towards Asia.
He wrote: "To handle these changes, it is ever more important that the United Kingdom develop closer foreign and security cooperation with the EU... Both parties must be honest about the gravity of this moment.
"From Ukraine to Gaza and the Sahel [troubled African countries that stretch the southern Sahara region], there is an arc of conflict and instability inside and near Europe’s borders that affects the United Kingdom and the continent’s interests equally.
"Yet the European Union and the British Government have no formal means of cooperation. To address that problem, the United Kingdom must seek a new geopolitical partnership with the EU."
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Shadow foreign secretary David Lammy said the UK "must seek a new geopolitical partnership with the EU"
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It comes after Shadow Northern Ireland Secretary Hilary Benn claimed the EU will breathe a "sigh of relief” if Labour leader Sir Keir Starmer wins the upcoming general election.
He said: "Brexit has of course affected politics in the UK. But it’s also affected politics in the European Union. The EU is a bit tired of negotiating with Britain.
"They’ve got lots of other things on their plate. And we have to recognise that while the EU has loads of experience of negotiating agreements with countries coming towards it, never before has it had to do a deal … with a big country that’s walked out.
"Now I am a great believer in the healing qualities of time. And there is no doubt that the arrival of a Labour Government, if we win … will be greeted in the EU with a big and audible sigh of relief."
Brexit-backing Home Secretary James Cleverly went one step further, claiming it showed Starmer "wants to rejoin the EU in all but name"
PAHousing Secretary Michael Gove claimed the remarks revealed "the real Keir Starmer" as he argued the lawyer-turned-politician wanted to "re-run the Brexit agonies of the past."
Brexit-backing Home Secretary James Cleverly went one step further, claiming it showed Starmer "wants to rejoin the EU in all but name."
Meanwhile, David Lammy accused the Conservatives of undermining the UK’s soft power by “attacking institutions such as universities, courts, and the BBC”.