Mr Sunak is reportedly weighing up some elements of the hardline plan proposed by Ms Braverman - whom he sacked earlier this week - to thwart fresh legal challenges to Rwanda flights after the Supreme Court deemed the plan "unlawful".
The Tory leader is considering an emergency bill that would deem Rwanda a "safe country" and attempt to make clear that this designation overrides the Human Rights Act, according to The Times.
Asked if he is comfortable with plans to create new legislation to overrule the Supreme Court, Mr Hunt told Sky News: "Yes, that is our democratic right as members of parliament."
A less contentious option is to try to designate Rwanda a "safe" country without any attempt to override human rights law, with the two possibilities said to be part of "live" discussions.
“With Rishi Sunak we have the most persistent and most determined Prime Minister I have ever worked with,” the Chancellor later told BBC Sunday with Laura Kuenssberg.
“When it comes to solving fearsomely complex problems, I never worked with anyone as phenomenal as Rishi … when you interview me next year, we will be having a discussion about how we succeeded in this plan.”
Grilled on whether the government could leave the ECHR, Mr Hunt said: “We don’t believe at this stage that that is necessary … We don’t believe it will come to that, at this stage – we don’t want to do that.”
However, the Chancellor added that the government was determined to stop “foreign judges” deciding who comes to the UK.
“In the end our bottom line is clear – it is elected representatives in parliament that should make the decision.”
It comes after Supreme Court judge Lord Sumption warned that the Rwanda plan is "probably dead" in its current form.
Asked by Trevor Phillips on the presenter's Sunday show on Sky News whether the scheme is "dead", he replied: "I think the current Rwanda scheme is probably dead, but we obviously have to suspend judgment until we see what this legislation or this new treaty looks like."
He also suggested judges in Strasbourg would come to a similar view of the scheme's legality as UK Supreme Court justices.
He said: "The Government have made clear ... that they don't intend to do that (withdraw from the European Convention on Human Rights). Although the Government may well ignore interim orders from Strasbourg, they presumably intend to comply with final orders from Strasbourg.
"It (the Strasbourg court) will investigate safety for itself and probably arrive at a conclusion very similar to that of the Supreme Court."
He also said he is "sceptical" of reported plans to send British civil servants to work in the east African country, adding: "The main problem (with the) scheme is that it outsources to Rwanda the decisionabout whether people have refugee status."