The prime minister is said be considering ways to prevent the legislation being used to stop deportations of asylum seekers and prosecutions of British soldiers.
A review of human rights laws has been carried out across Whitehall and its findings will be announced “in the coming weeks”, the Daily Telegraph reported.
The move comes after Mr Johnson sparked fury in Europe with the Internal Market Bill to override part of the Brexit deal he signed in October.
Ministers have admitted that it would break international law but the prime minister claims it is necessary to prevent the EU “carving up our country”.
However he is facing mounting criticism from across the political spectrum, including rebel Tory MPs and former prime ministers John Major and Tony Blair.
Brussels wants the UK to commit to the European Convention on Human Rights as part of the terms of a Brexit trade agreement.
However UK negotiators have refused, claiming that the issue is a matter of “sovereignty”.
The possibility of opting out of the Human Rights Act once Britain had left the EU was raised when Theresa May was prime minister. She said during her leadership campaign in 2016 that the ECHR had made it harder to deport terror suspects and criminals.
Mr Johnson’s chief adviser Dominic Cummings is also a critic, saying in 2018 that a referendum on the ECHR would be “high on the agenda” .
The Tory election manifesto last year pledged to “update” the act after Brexit and in February it was reported that ministers were also looking at potentially suspending the ECHR.
Then in May Michael Gove admitted that the UK was refusing to sign up to human rights safeguards as part of a trade deal so that the government has the option of changing the Human Rights Act.
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