EU diplomats are said to have privately warned the UK not to withdraw from the international human rights agreements, such as the ECHR and the UN Refugee convention.
The UK is currently weighing up plans to backtrack on the agreements, in order to get the Rwanda migrant plan off the ground.
Immigration Minister Robert Jenrick, former Home Secretary Suella Braverman and a significant number of backbenchers on the right of the party are pressing the Government to withdraw from the agreements.
But Home Secretary James Cleverly and Foreign Secretary David Cameron, who both came to post after Braverman was sacked, are more reluctant to do so, partly due to concerns over how it might impact the UK's international relations.
WATCH: James Cleverly says nothing in Rwanda ruling dims party's commitment to the plan
Sources told Bloomberg that EU officials, along with some member states, have raised concerns over the move with their British counterparts.
The message is said to have been sent from the EU to the UK repeatedly, and at multiple levels.
Earlier this month, the Supreme Court ruled that the plan to send migrants to Rwanda is unlawful.
All five justices unanimously agreed with the Court of Appeal’s conclusion that the Rwanda policy was unlawful.
Delivering his judgement, Lord Reed noted that "the court of appeal was right to overturn the high court's decision and to consider the evidence again for itself".
He cited concerns about "media and political freedom", the country's "poor human rights record" and a "misunderstanding of its obligations under the Refugee Convention".
Speaking after the ruling, the Prime Minister said the Government will "carefully review" the judgement and make plans for "next steps".
Cleverly has indicated reluctance after he urged people not to "fixate" on the plans.
He also said that leaving the European Convention on Human Rights would undermine attempts to stop the boats.
The Government is expected to unveil fresh plans to tackle legal migration and to get the Rwanda scheme off the ground in the coming weeks.
Speaking after the Rwanda verdict, Sunak said he will "not allow a foreign court to block these flights".
The PM said: “We must be honest about the fact that even once Parliament has changed the law here at home, we could still face challenges from the European Court of Human Rights in Strasbourg.
“I told Parliament earlier today that I’m prepared to change our laws and revisit those international relationships to remove the obstacles in our way.
MIGRATION FURY:
Speaking after the Rwanda verdict, Sunak said he will "not allow a foreign court to block these flights"
PA
“So let me tell everybody now, I will not allow a foreign court to block these flights.
“If the Strasbourg court chooses to intervene against the expressed wishes of Parliament, I am prepared to do what is necessary to get flights off. I will not take the easy way out.
“Because I fundamentally do not believe that anyone thinks the founding aims of the European Convention on Human Rights was to stop a sovereign Parliament removing illegal migrants to a country deemed to be safe in parliamentary statute and binding international law.”
