Justice Secretary David Lammy and Attorney General Lord Hermer have travelled to Strasbourg to take part in the talks.
Lammy is expected to say: “The definition of ‘family life’ can’t be stretched to prevent the removal of people with no right to remain in the country… the threshold of ‘inhuman and degrading treatment’ must be constrained to the most serious issues… and states must be able to take proportionate decisions on the removal of foreign criminals.”
He will say that the convention is “a critical foundation of peace, stability, and security in Europe” but will add that it was “never intended to be frozen in time”.
The BBC understands that the aim is for member states to reach a political declaration by the spring which would set how the ECHR is applied in migration cases.
If such an agreement were achieved, it could be one of the most important reforms to how human rights law is applied in the 75-year history of the convention.
The meeting at the Council of Europe, the political body that agrees the human rights laws which are then applied by the court, comes after months of pressure over migration.
Nine members of the human rights body, led by Italy and Denmark, called earlier this year for reforms.
The UK did not sign that open letter – but it has been lobbying behind the scenes for talks on reforms.
Membership of the convention has become increasingly contentious in the UK in recent years.
Both the Conservatives and Reform UK have said they would leave it if they won the next election.
Kemi Badenoch has said leaving would not be a “silver bullet” but was a necessary step to “protect our borders, our veterans and our citizens”.
Liberal Democrat leader Sir Ed Davey said he would oppose such a move saying the convention “upholds our freedom” and would “do nothing to stop the boats or fix our broken immigration system”.
