The Home Secretary has reportedly ignored requests by the Archbishop of Canterbury to meet.
The House - the magazine of the Houses of Parliament - reports that Archbishop Justin Welby has "reached out a number of times" to Suella Braverman's office about meeting.
A spokesman for the Archbishop told the magazine, "The Archbishop would be happy to meet the Home Secretary to discuss issues of mutual interest and concern.
"In the past, the Archbishop has met other home secretaries. It is not unusual."
Archbishop Welby has been an outspoken critic of the government's immigration policy, specifically plans to send migrants to Rwanda.
In July, Welby spearheaded an amendment to the Illegal Migration Bill forcing the government to devise a 10-year strategy on how to work with international partners in addressing the refugee crisis and human trafficking.
Speaking earlier in the debate, he called the bill "isolationist", "morally unacceptable" and "politically impractical".
Braverman has claimed that many of the people crossing the English Channel in small boats are "gaming the system" and lie about their personal circumstances, like age or religion.
"Many of these people are gaming the system. We know that they will lie about their ages," she said during an appearance on GB News.
"We know that in about 50 per cent of cases when we challenge the age, the Government is right and the claimants are wrong, and they are actually adults pretending to be children.
"They may lie about their religion, they may lie about being married to someone or having a family member here.
"So there is a lot of gaming of our system, and we need to inject more rigour and robustness into our framework. And actually deterrents - and that is why our partnership with Rwanda is absolutely central to solving this problem."
