The Conservatives have said the Human Rights Act should no longer apply to immigration decisions.
They are calling for a change in the law that would stop people challenging their deportation on human rights grounds in the UK courts.
Leader Kemi Badenoch has previously criticised how some foreign criminals and illegal migrants were using the act to avoid deportation.
A Home Office source told the BBC the Conservatives had left the asylum system in chaos and their suggestion would be totally unworkable.
The Human Rights Act was passed by a previous Labour government, and incorporates the European Convention on Human Rights (ECHR) into British law.
The ECHR has been a hotly debated topic within the Conservative Party – with some on the right wanting the UK to pull out of the treaty completely.
The act has been used to halt attempts to deport migrants deemed to be in the UK illegally, and it stopped flights carrying asylum seekers taking off for Rwanda.
Badenoch has not proposed leaving the ECHR, but has argued some foreign criminals and migrants in the UK illegally have successfully used the act to avoid deportation – saying, for example, this would undermine their right to family life.
She also believes some judges generously interpret the provisions of the act when rejecting deportation.
The Conservatives are suggesting an amendment to the government’s Border Security, Asylum and Immigration Bill – which is currently at the committee stage – that would disapply the act in immigration cases.
The policy would give her a clear political dividing line with Labour.
Under the ECHR, migrants could still appeal against deportation to the European Court of Human Rights in Strasbourg.
Cabinet Office Minister Pat McFadden told the BBC’s Sunday with Laura Kuenssberg that the Conservatives’ proposal “looks like an outsourcing” of immigration decisions to the Strasbourg court.
“I don’t think that really deals with the issue and I’m afraid it’s symptomatic of the kind of gimmicks without action that we saw for a long, long period of time,” he said.
Later in the programme, Shadow Home Secretary Chris Philp defended the proposal, saying it would make a “very big difference”. He said judges have expanded definitions under the EHCR “in ways that defy common sense”.
“Of course we believe in rights, but where you have courts just constantly expanding the definition in a way that was never contemplated at the beginning…it gets out of hand,” he said.
Philp said membership in the ECHR requires “proper consideration”, which the Conservatives will be thinking about “in a very carefully considered manner in the coming months”.
Badenoch said the amendment she is suggesting would be “critical to shift immigration powers from the courts to Parliament and elected ministers, enabling more effective control over our borders”.
“Operating in Britain’s national interest means recognising the government’s primary purpose: defending our borders, values, and people. Our amendment aims to restore control and prioritise national security,” she said.
The Home Office source said: “The Tories left the asylum system in utter chaos.
“They had 14 years to make changes and instead spent hundreds of millions of pounds on the failed Rwanda scheme, as small boat crossings hit a record high.
“This amendment is totally unworkable.
“Instead of dealing with mad proposals that will never work, the Labour government is getting a grip of the asylum system, increasing removals of those with no right to be here, saving millions on asylum hotels and looking at ways of tightening the application of Article 8 to ensure the system works more effectively.”
The ECHR was established in 1950 by a number of countries including the UK.
The treaty, which sets out the rights and freedoms people are entitled to in the 46 signatory countries, is overseen by the European Court of Human Rights in Strasbourg.
It is separate to the European Union – so the UK remained part of both after Brexit.
